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beruecksichtige naturwissenschaftliche Journale:
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JOMC publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals.
Aktuelle wissenschaftliche Fachartikel der
genannten Journale:
Accurate treatment of electron correlation in quantum chemistry requires solving the many-electron problem. If the nodal surface
of a many-electron wave function is available even in an approximate form, the fixed-node diffusion Monte Carlo (FNDMC) approach
from the family of quantum Monte Carlo methods can be successfully used for this purpose. The issue of description and classification
of nodal surfaces of fermionic wave functions becomes central for understanding the basic properties of many-electron wave
functions and for the control of accuracy and computational efficiency of FNDMC computations. In this work, we approach the
problem of automatic classification of nodal pockets of many-electron wave functions. We formulate this problem as that of
binary classification and apply a number of techniques from the machine learning literature. We apply these techniques on
a range of atoms of light elements and demonstrate varying degrees of success. We observe that classifiers with relatively
simple geometry perform poorly on the classification task; methods based on a random collection of tree-based classifiers
appear to perform best. We conclude with thoughts on computational challenges and complexity associated with applying these
techniques to heavier atoms.
Content Type Journal Article
Category Original Paper
Pages 1-8
DOI 10.1007/s10910-012-0019-5
Authors
Erin LeDell, Division of Biostatistics, UC Berkeley, Berkeley, CA 94720, USA
Prabhat, Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Dmitry Yu. Zubarev, Department of Chemistry, UC Berkeley, Berkeley, CA 94720, USA
Brian Austin, National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
William A. Lester Jr., Department of Chemistry, UC Berkeley, Berkeley, CA 94720, USA
The aim of the paper is to investigate the global dynamics of mathematical models for a continuous flow bioreactor and a membrane
reactor. It assumes that the models include terms representing death of the microorganism and maintenance energy, respectively.
By carrying out a qualitative analysis of the models, we give the classification of the equilibria and show that an unstable
limit cycle can exist when the non-washout equilibrium is a focus.
Content Type Journal Article
Category Original Paper
Pages 1-9
DOI 10.1007/s10910-012-0027-5
Authors
Tonghua Zhang, Mathematics, H38, FEIS, Swinburne University of Technology, Hawthorn, VIC 3122, Australia
High Dimensional Model Representation (HDMR) based methods are used to generate an approximation for a given multivariate
function in terms of less variate functions. This paper focuses on Hybrid HDMR which is composed of Plain HDMR and Logarithmic
HDMR. The Plain HDMR method works well for representing multivariate functions having additive nature. If the function under
consideration has a multiplicative nature, then the Logarithmic HDMR method produces better approximation. Hybrid HDMR method
aims to successfully represent a multivariate function having neither purely additive nor purely multiplicative nature under
a hybridity parameter. The performance of the Hybrid HDMR method strongly depends on the value of this hybridity parameter
because this parameter manages the contribution level of Plain and Logarithmic HDMR expansions. The main purpose of this work
is to optimize the hybridity parameter to get the best approximations. Fluctuationlessness Approximation Theorem is used in
this optimization process and in evaluating the multiple integrals appearing in HDMR based methods. A number of numerical
implementations are given at the end of the paper to show the performance of our proposed method.
Content Type Journal Article
Category Original Paper
Pages 1-16
DOI 10.1007/s10910-012-0026-6
Authors
Burcu Tunga, Faculty of Computer and Informatics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
Metin Demiralp, Informatics Institute, Computational Science and Engineering Program, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
The stereoisogram approach (Fujita in J Org Chem 69:3158â3165, 2004; and in Tetrahedron 60:11629â11638, 2004) has been applied to comprehensive discussions on geometric aspects and stereoisomeric aspects of stereochemistry, where
a prismane skeleton has been selected as a rigid skeleton for the underlying proligand-promolecule model. The existence of
five types of stereoisograms (Types IâV) has been demonstrated by using prismane derivatives as illustrative examples in a
consistent way with a general proof using the group theory (Fujita in MATCH Commun Math Comput Chem 54:39â52, 2005). After a C/A-convention for characterizing absolute configurations was proposed on the basis of the stereoisogram approach, such geometric
and stereoisomeric aspects of stereochemistry as chirality, RS-stereogenicity, and sclerality have been discussed by putting emphasis on the independence between chirality and RS-stereogenicity, on extended features of pseudoasymmetry, and on the assignability of A/C-descriptors. By following a general rationalization (Fujita in Tetrahedron 62:691â705, 2006), prochirality, pro-RS-stereogenicity, and prosclerality have been discussed on the basis of such attributive terms as sphericities, RS-tropicities, and cercalities, where illustrative examples are selected from prismane derivatives. Thereby, the stereoisogram
approach has been clarified to be a versatile device for integrating geometric and stereoisomeric aspects of stereochemistry.
Content Type Journal Article
Category Original Paper
Pages 1-34
DOI 10.1007/s10910-012-0024-8
Authors
Shinsaku Fujita, Shonan Institute of Chemoinformatics and Mathematical Chemistry, Kaneko 479-7, Ooimachi, Ashigara-Kami-Gun, Kanagawa 258-0019, Japan
Highly accurate 2-body reduced density matrices of atoms and molecules have been directly determined without calculation of
their wave functions with the use of the G-particle-hole hypervirial (GHV) equation method (Alcoba et al. in Int. J. Quantum Chem. 109:3178, 2009). Very recently, the computational efficiency of the GHV method has been significantly enhanced through the use of sum factorization
and matrix-matrix multiplication (Alcoba et al. in Int. J. Quantum Chem 111:937, 2011). In this paper, a detailed analysis of the matrix contractions involved in GHV calculations is carried out. The analysis
leads to a convenient strategy for exploiting point group symmetry, by which the computational efficiency of the GHV method
is further improved. Implementation of the symmetry-adapted formulation of the method is reported. Computer timings and hardware
requirements are illustrated for several representative chemical systems. Finally, the method is applied to the well-known
challenging calculation of the torsional potential in ethylene.
Content Type Journal Article
Category Original Paper
Pages 1-13
DOI 10.1007/s10910-012-0023-9
Authors
Gustavo E. Massaccesi, Departamento de Ciencias Exactas, Ciclo BĂĄsico ComĂşn, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Diego R. Alcoba, Departamento de FĂsica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Ofelia B. OĂąa, Instituto de Investigaciones FisicoquĂmicas TeĂłricas y Aplicadas, CCT La Plata, Consejo Nacional de Investigaciones CientĂficas y TĂŠcnicas, Universidad Nacional de La Plata, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
Among the four methods of the unit-subduced-cycle-index (USCI) approach (Fujita in Symmetry and Combinatorial Enumeration
in Chemistry. Springer, Berlin, Heidelberg, 1991), the fixed-point-matrix (FPM) method and the partial-cycle-index (PCI) method have been applied to the combinatorial enumeration
of prismane derivatives. These enumeration processes are based on the proligand-promolecule model, which enables us to take
account of achiral and chiral proligands. Prochirality in a geometric meaning has been discussed in general by emphasizing
the presence of enantiospheric orbits in enumerated prismane derivatives. An enantiospheric orbit accommodating chiral proligands
(along with achiral ones) has been shown to exhibit prochirality by using various prismane derivatives as examples. On the
other hand, the scope of pseudoasymmetry has been extended to cover such a rigid skeleton as prismane in addition to a usual
pseudoasymmetric center as a single atom, where the proligand-promolecule model plays an essential role.
Content Type Journal Article
Category Original Paper
Pages 1-21
DOI 10.1007/s10910-012-0025-7
Authors
Shinsaku Fujita, Shonan Institute of Chemoinformatics and Mathematical Chemistry, Kaneko 479-7 Ooimachi, Ashigara-Kami-Gun, Kanagawa-Ken, 258-0019 Japan
Various sorts of isomer enumeration problems are addressed in the context of polycarboranes, with special illustrative focus
on the case of dicarboranes, for which then various numerical results are given. A systematic and general PĂłlya-theoretic
methodology is used to make the computations, including some new techniques being applicable to a wide range of nano-structures
built from a framework of like local subunits.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-012-0017-7
Authors
Vladimir R. Rosenfeld, Texas A&M University, Galveston, TX 77553, USA
Douglas J. Klein, Texas A&M University, Galveston, TX 77553, USA
Josep M. Oliva, Instituto de QuĂmica-FĂsica âRocasolanoâ, CSIC, Serrano, 119, 28006 Madrid, Spain
It is shown that a direct method for bound states can give the integrated probability over a given region and also the normalised
squared wavefunction at a given point without using any quadratures or wavefunction storage. The method is tested on a known
example and is then applied to an asymmetric double well potential and also to find the probability of penetration of a particle
into the non-classical region for a single well potential.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-012-0020-z
Authors
J. P. Killingbeck, Institut UTINAM (CNRS UMR 6213), 41bis Avenue de lâObservatoire, BP 1615, Besancon Cedex, 25010 France
A. Lakhlifi, Institut UTINAM (CNRS UMR 6213), 41bis Avenue de lâObservatoire, BP 1615, Besancon Cedex, 25010 France
Non-homogeneous velocity distribution of the flow in the channel of a single-screw extruder is taken into account by a new
model developed on the basis of the Markov chains. This model allows calculating the Residence Time Distribution (RTD) as
well as the influence of the operating conditions on the process at any velocity distribution in the channel. It has been
used to represent experimental results on mass flow rate and RTD previously obtained by extrusion of an acrylic polymer, Eudragit
E100, at different temperatures and screw rotation speeds. The diffusion coefficient is the only adjusting parameter of the
model. It was shown that it does not depend on the screw rotation speed and a correlation between this diffusion coefficient
and the barrel temperature was found. The model provides global understanding of the transport kinetics of the flowing material
through the extruder according to its behaviour and better describes the progress of the polymer flow all along the barrel
from the hopper to the die.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-012-0022-x
Authors
Denis Ponomarev, Ecole des Mines dâAlbi, RAPSODEE Research Centre, CNRS, UniversitĂŠ de Toulouse, 81013 Albi, France
Elisabeth Rodier, Ecole des Mines dâAlbi, RAPSODEE Research Centre, CNRS, UniversitĂŠ de Toulouse, 81013 Albi, France
Martial Sauceau, Ecole des Mines dâAlbi, RAPSODEE Research Centre, CNRS, UniversitĂŠ de Toulouse, 81013 Albi, France
ClĂŠmence Nikitine, Ecole des Mines dâAlbi, RAPSODEE Research Centre, CNRS, UniversitĂŠ de Toulouse, 81013 Albi, France
Vadim Mizonov, Department of Applied Mathematics, Ivanovo State Power Engineering University, Rabfakovskaya 34, 153003 Ivanovo, Russia
Jacques Fages, Ecole des Mines dâAlbi, RAPSODEE Research Centre, CNRS, UniversitĂŠ de Toulouse, 81013 Albi, France
In this paper we investigate the properties of the travelling combustion wave solutions in a diffusion-thermal model with
a two-step competitive exoâendothermic reaction mechanism in one spatial dimension under adiabatic conditions. The model is
analysed both numerically and analytically using asymptotic analysis. It is demonstrated that depending on the parameter values,
the flame speed as a function of parameters is either a single-valued monotonic function or a double-valued c-shaped function
with the turning point type of behaviour. For the case of single-valued flame speed, two flame regimes are identified: the
regime with exo- and endothermic reaction domination. Two different routes to extinction are found as well as regions of the
existence of combustion waves in the parameter space. Prospects of further work are also discussed.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-012-0021-y
Authors
V. V. Gubernov, I.E. Tamm Theory Department, P.N. Lebedev Physical Institute, 53 Leninsky Prospect, 119991 Moscow, Russia
J. J. Sharples, Applied and Industrial Mathematics Research Group, School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra, Australia
H. S. Sidhu, Applied and Industrial Mathematics Research Group, School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra, Australia
A. C. McIntosh, Energy and Resources Institute, School of Process, Environmental and Materials Engineering, University of Leeds, Leeds, UK
J. Brindley, School of Mathematics, University of Leeds, Leeds, UK
The maximization of the efficiency of a hybrid two-step method for the numerical solution of the radial SchrĂśdinger equation
and related problems with periodic or oscillating solutions via the procedure of vanishing of the phase-lag and its derivatives
is studied in this paper. More specifically, we investigate the vanishing of the phase-lag and its first and second derivatives
and how this disappearance maximizes the efficiency of the hybrid two-step method.
Content Type Journal Article
Category Original Paper
Pages 1-21
DOI 10.1007/s10910-012-0008-8
Authors
Ibraheem Alolyan, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451 Saudi Arabia
T. E. Simos, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451 Saudi Arabia
We investigate the complexity of the hydrogenic identity SN2 exchange reaction by means of information-theoretic functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e., the IâD, DâL and IâJ planes and the FisherâShannon (FS) and LĂłpez-Mancini-Calbet (LMC) shape complexities. The several information-theoretic measures
of the one-particle density were computed in position (r) and momentum (p) spaces. The analysis revealed that the chemically significant regions of this reaction can be identified through most of
the information-theoretic functionals or planes, not only the ones which are commonly revealed by the energy, such as the
reactant/product (R/P) and the transition state (TS), but also those that are not present in the energy profile such as the
bond cleavage energy region (BCER), the bond breaking/forming regions (BâB/F) and the charge transfer process (CT). The analysis
of the complexities shows that the energy profile of the identity SN2 exchange reaction bears no simple behavior with respect to the LMC and FS measures. Most of the chemical features of interest
(BCER, BâB/F and CT) are only revealed when particular information-theoretic aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.
Content Type Journal Article
Category Original Paper
Pages 1-19
DOI 10.1007/s10910-012-0009-7
Authors
Moyocoyani Molina-EspĂritu, Departamento de QuĂmica, Universidad AutĂłnoma Metropolitana-Iztapalapa, 09340 Mexico, D.F., Mexico
Rodolfo O. Esquivel, Departamento de QuĂmica, Universidad AutĂłnoma Metropolitana-Iztapalapa, 09340 Mexico, D.F., Mexico
Juan Carlos Angulo, Departamento de FĂsica AtĂłmica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
Juan AntolĂn, Instituto Carlos I de FĂsica TeĂłrica y Computacional, Universidad de Granada, 18071 Granada, Spain
JesĂşs S. Dehesa, Departamento de FĂsica AtĂłmica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
A noncentral ring-shaped potential is proposed in which the noncentral electric dipole and a novel angle-dependent component
are included, the radial part is selected as the Coulomb potential or the harmonic oscillator potential. The exact solution
of the SchrĂśdinger equation with this potential is investigated by working in a complete square integrable basis that supports
a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relation for the expansion coefficients
of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre
polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation.
Content Type Journal Article
Category Original Paper
Pages 1-13
DOI 10.1007/s10910-012-0015-9
Authors
Guo-Qing Huang-Fu, Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan, 714000 Peopleâs Republic of China
Min-Cang Zhang, College of Physics and Information Technology, Shaanxi Normal University, Xiâan, 710062 Peopleâs Republic of China
The native states of the most compact globular proteins have been described as being in the so-called âcollapsed-polymer regime,â
characterized by the scaling law Rg ~ nν, where Rg is radius of gyration, n is the number of residues, and ν â 1/3. However, the diversity of folds and the plasticity of native states suggest that
this law may not be universal. In this work, we study the scaling regimes of: (i) one to four-domain protein chains, and (ii) their constituent domains, in terms of the four major folding classes. In the case of complete chains, we show that size
scaling is influenced by the number of domains. For the set of domains belonging to the all-ι, all-β, ι/β, and ι + β folding classes, we find that size-scaling exponents vary between 0.3 ⤠ν ⤠0.4. Interestingly, even domains in the same
folding class show scaling regimes that are sensitive to domain provenance, i.e., the number of domains present in the original intact chain. We demonstrate that the level of compactness, as measured by
monomer density, decreases when domains originate from increasingly complex proteins.
Content Type Journal Article
Category Original Paper
Pages 1-19
DOI 10.1007/s10910-012-0010-1
Authors
Parker Rogerson, DĂŠpartement de Chimie et Biochimie and Biomolecular Sciences Program, Laurentian University, Ramsey Lake Road, Sudbury, ON P3E 2C6, Canada
Gustavo A. Arteca, DĂŠpartement de Chimie et Biochimie and Biomolecular Sciences Program, Laurentian University, Ramsey Lake Road, Sudbury, ON P3E 2C6, Canada
An algorithm is presented for the estimation of molecular properties over a library built around a scaffold, which has N sites for functionalization with Mi moieties at the ith scaffold site, corresponding to a library of
N Ă i=1
Mi
molecules. The algorithm relies on a series of operations involving (i) synthesis and property measurement of a minimal number
of T randomly sampled members of the library, (ii) expression of the observed property in terms of a high-dimensional model representation
(HDMR) of the moiety â property map, (iii) optimization of the ordered sequence of moieties on each site to regularize the
HDMR map and (iv) interpolation using the map to estimate the properties of as yet unsynthesized compounds. The set of operations
is performed iteratively aiming to reach convergence of the predictive HDMR map with as few synthesized samples as possible.
Through simulation, the number T of required random molecular samples is shown to scale very favorably with
T < <
N Ă i=1
Mi
for cases up to N = 20 and Mi = 20. For example, high estimation quality was attained for simulated libraries with T ~ 5,000 sampled compounds for a library of 2012 members and T ~ 12,500 sampled compounds for a library of 2020 members. The algorithm is based on the assumption that a systematic pattern exists in the moiety â property map provided
that the moieties are optimally ordered on the scaffold sites within the context of HDMR. The overall procedure is referred
to as the substituent reordering HDMR algorithm (SR-HDMR). The technique was also successfully tested with laboratory data
for estimating C13-NMR shifts in a tri-substituted benzene library and for lac operon repression binding.
Content Type Journal Article
Category Original Paper
Pages 1-26
DOI 10.1007/s10910-012-0005-y
Authors
Sofia Izmailov, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
XiaoJiang Feng, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
Genyuan Li, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
Herschel Rabitz, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
D-MORPH regression is a procedure for the treatment of a model prescribed as a linear superposition of basis functions with
less observation data than the number of expansion parameters. In this case, there is an infinite number of solutions exactly
fitting the data. D-MORPH regression provides a practical systematic means to search over the solutions seeking one with desired
ancillary properties while preserving fitting accuracy. This paper extends D-MORPH regression to consider the common case
where there is more observation data than unknown parameters. This situation is treated by utilizing a proper subset of the normal equation of
least-squares regression to judiciously reduce the number of linear algebraic equations to be less than the number of unknown parameters, thereby permitting application of D-MORPH regression. As a result, no restrictions
are placed on model complexity, and the model with the best prediction accuracy can be automatically and efficiently identified.
Ignition data for a H2/air combustion model as well as laboratory data for quantum-control-mechanism identification are used to illustrate the method.
Content Type Journal Article
Category Original Paper
Pages 1-18
DOI 10.1007/s10910-012-0004-z
Authors
Genyuan Li, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
Roberto Rey-de-Castro, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
Herschel Rabitz, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
The stereoisogram approach (Fujita in J Org Chem 69:3158â3165, 2004, Tetrahedron 62:691â705, 2006, Tetrahedron 65:1581â1592, 2009) is applied to trigonal bipyramidal compounds, where chiral and achiral proligands are taken into consideration. After configurations
of trigonal bipyramidal compounds are enumerated by using the partial-cycle-index method (Fujita in Symmetry and combinatorial
enumeration in chemistry. Springer, Berlin, 1991), they are categorized into Type IâV cases according to the stereoisogram approach. The enumerated configurations are specified
by configuration indices and C/A-descriptors, which are assigned in terms of RS-diastereomeric relationships, (not of enantiomeric relationships). The concept of a multiplet of stereoisograms is proposed to formulate the concept of ortho-stereogenicity, which is concerned with ortho-diastereomeric relationships between stereoisograms. On the other hand, the concept of stereogenicity (which has been used in the conventional stereochemistry) is redefined by starting from RS-stereogenicity and by comparing with the ortho-stereogenicity, where the stereogenicity is concerned with diastereomeric relationships between pairs of enantiomers. Berryâs pseudorotation for isomerization of trigonal bipyramidal compounds is reinterpreted
in order to cover more general cases in which chiral moieties along with achiral moieties (i.e., all of Type IâV cases) are
taken into consideration. A modified Desargues-Levi graph is proposed to cover Type IâV cases. In addition, an adamantane-like
graph is proposed to formulate Berryâs pseudorotation on the basis of a multiplet of stereoisograms, where quadruplets of
RS-stereoisomers occupy the nodes of the graph. Thereby, a multiplet of stereoisograms is shown to be a versatile tool to characterize
stereoisomerization processes of inorganic stereochemistry in addition to those of organic stereochemistry.
Content Type Journal Article
Category Original Paper
Pages 1-46
DOI 10.1007/s10910-012-0007-9
Authors
Shinsaku Fujita, Shonan Institute of Chemoinformatics and Mathematical Chemistry, Kaneko 479-7, Ooimachi, Ashigara-Kami-Gun, Kanagawa-Ken 258-0019, Japan
Approximate analytical bound state solutions of the radial SchrĂśdinger equation are studied for a two-term diatomic molecular
potential in terms of the hypergeometric functions for the cases where q ⼠1 and q = 0. The energy eigenvalues and the corresponding normalized wave functions of the ManningâRosen potential, the âstandardâ
HulthĂŠn potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical
results are the same with the ones obtained before.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-012-0011-0
Authors
AltuÄ Arda, Department of Physics Education, Hacettepe University, 06800 Ankara, Turkey
Ramazan Sever, Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
The model presented accounts for the diffusion of a reactant and of charge carriers within the modifier layer placed at electrode
surface, and redox interaction between reactant and an active center bearing charge carriers. The study extends our previous
model by the use of a combination of two kinds of redox interactionâa simple chemical second-order reaction, and Michaelis-type
redox reaction. Depending on relative increments from these two kinetic models, either linear, or hyperbolic dependencies
of electric current on reactant concentration were obtained. The results obtained have been analyzed in terms of current-concentration
interdependencies.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-012-0016-8
Authors
Mantas Puida, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
Albertas Malinauskas, Institute of Chemistry, Center of Physical and Technology Sciences, GoĹĄtauto 9, 01108 Vilnius, Lithuania
Feliksas Ivanauskas, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum.
The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also considered.
Algebraic method is used in the calculations.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-012-0013-y
Authors
Huseyin Akcay, Faculty of Engineering, BaĹkent University, BaglÄąca Campus, Ankara, Turkey
Ramazan Sever, Department of Physics, Faculty of Arts and Sciences, Middle East Technical University, 06531 Ankara, Turkey
The stereoisogram approach, which has originally been developed to rationalize organic stereochemistry (Fujita in J Org Chem
69:3158â3165, 2004; Fujita in Tetrahedron 62:691â705, 2006; 65:1581â1592, 2009), is extended and applied to inorganic stereochemistry by using trigonal bipyramidal compounds as examples. The point group
D3h of a trigonal bipyramidal skeleton is extended into the RS-stereoisomeric group of order 24, which is considered to control a stereoisogram of the trigonal bipyramidal skeleton. Stereoisograms
of trigonal bipyramidal compounds derived from the skeleton correspond to subgroups of the RS-stereoisomeric group. Thereby, they are discussed in terms of attributive terms (chirality/achirality, RS-stereogenicity/RS-astereogenicity, and sclerality/asclerality) or equivalently in terms of relational terms (enantiomeric/self-enantiomeric,
RS-diastereomeric/self-RS-diastereomeric, and holantimeric/self-holantimeric), where the stereoisograms are categorized into five types (Types IâV).
Among them, stereoisograms of Types I, III, and V are shown to be capable of giving C/A-descriptors because of their RS-stereogenicity (or RS-diastereomeric relationships).
Content Type Journal Article
Category Original Paper
Pages 1-24
DOI 10.1007/s10910-012-0006-x
Authors
Shinsaku Fujita, Shonan Institute of Chemoinformatics and Mathematical Chemistry, Kaneko 479-7, Ooimachi, Ashigara-Kami-Gun, Kanagawa-Ken 258-0019, Japan
This project aims at computation excited-state energy eigenvalues and wave-function of a particle under Gaussian asymmetric
double-well potential using numerical shooting method and perturbation theory a method to deal with discrete-eigenvalue problems.
We also compare the energy eigenvalue and wave-function with those obtained from other typical means popular among physics
students, namely the numerical shooting method and perturbation theory. Show that the idea of program of the numerical shooting
method and perturbation theory of this problem (see Sects. 2.1 and 4) The numerical shooting method is generally regarded
as one of the most efficient methods that give very accurate results because it integrates the SchrĂśdinger equation directly,
though in the numerical sense. The n = even case is shown in Figs. 4, 5 and 6. In this case, the wave-function has split up on asymmetric nodes under Gaussian
asymmetric double-well potential. The n = odd case is shown in Fig. 7. In this case, the wave-function has not split up on asymmetric nodes under Gaussian asymmetric
double-well potential.
Content Type Journal Article
Category Original Paper
Pages 1-17
DOI 10.1007/s10910-012-9998-5
Authors
Sutee Boonchui, Forum for Theoretical and Computational Physics Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
Artit Hutem, Forum for Theoretical and Computational Physics Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
In this work we study the higher excited states of Helium Atom. The purpose is to evaluate Coulomb and exchange integral via
spherical harmonics series. The Coulomb and exchange integrals energy shift is evaluated up to sixth order. This is the energy
when the atom is perturbed by Coulomb potential between electrons. The energy levels obtained from both integrals are in agreement
with the experimental data. For highly-excited states, the calculated energy approaches â54.416 eV, in agreement with the
graphical results from the book by Powell and Crasemann [1].
Content Type Journal Article
Category Original Paper
Pages 1-17
DOI 10.1007/s10910-012-9997-6
Authors
Artit Hutem, Forum for Theoretical and Computational Physics Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
Sutee Boonchui, Forum for Theoretical and Computational Physics Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
In this work we consider explicit symplectic partitioned RungeâKutta methods with five stages for problems with separable
Hamiltonian. We construct three new methods, one with constant coefficients of eight phase-lag order and two phase-fitted
methods.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-012-0003-0
Authors
Th. Monovasilis, Department of International Trade, Technological Educational Institution of Western Macedonia at Kastoria, P.O. Box. 30, 52100 Kastoria, Greece
Using the theory of actions of groups on sets this paper describes an efficient method to obtain the partition of the symmetric
powers of a G-set into orbits, where G is a finite group. In this method, a generating function is obtained for each representative of the conjugacy classes of
subgroups of G. The coefficients of the generating function corresponding to a representative subgroup H ⤠G give the number of orbits isomorphic to the coset G/H that are contained in the successive symmetric powers of the G-set. A direct application of this approach is the attainment of the number and isotropy group of the vibrational force constants
associated with a set of internal coordinates for a given molecule. As illustration, the method has been applied to XYZ3 (C3v) molecules.
Content Type Journal Article
Category Original Paper
Pages 1-9
DOI 10.1007/s10910-012-0002-1
Authors
Emilio MartĂnez Torres, Department of Physical Chemistry, Facultad de EducaciĂłn, University of Castilla-La Mancha, Ronda de Calatrava, 3, 13003 Ciudad Real, Spain
This work aims to develop a new High Dimensional Model Representation (HDMR) based method which can construct an analytical
structure for a given multivariate data modelling problem. Modelling multivariate data through a divide-and-conquer method
stands for multivariate data partitioning process in which we deal with a number of less variate data sets instead of a single
N dimensional problem. Generalized HDMR is one of these methods used to model a multivariate data set which has a number of
scattered nodes with associated function values. However, Generalized HDMR includes a linear equation system with huge number
of unknowns and equations to be solved. This equation sometimes has linearly dependent equations in it and this is an undesirable
situation. This work offers a new method named Piecewise Generalized HDMR method which bypasses this disadvantage as well
as reducing the mathematical complexity and CPU time needed to complete the algorithm of the previous method. Our new method
splits the given problem domain into subdomains, applies the Generalized HDMR philosophy to each subdomain and superpositions
the information coming from these subdomains. The algorithm of this new method and a number of numerical implementations are
given in this paper.
Content Type Journal Article
Category Original Paper
Pages 1-16
DOI 10.1007/s10910-012-0001-2
Authors
M. Alper Tunga, Software Engineering Department, Faculty of Engineering, BahçeĹehir University, BeĹiktaĹ, 34349 Istanbul, Turkey
Metin Demiralp, Informatics Institute, Computational Science and Engineering Program, Ä°stanbul Technical University, Maslak, 34469 Istanbul, Turkey
Valley-ridge inflection points (VRI) on the potential energy surface for the ring opening of the cyclopropyl radical to the
allyl radical are determined using the tool of Newton trajectories (NTs) (Quapp and Schmidt in Theor Chem Acc 128:47, 2011). The UHF surface is treated in a former paper (Quapp et al. in Theor Chem Acc 129:803, 2011). This paper is the extension to the more expensive CASSCF(3,3) surface. We compare the results on the UHF surface with the
more appropriate calculation: there are quantitative as well as qualitative changes, of course. But many fundamental relations
are the same on both surfaces. However, we could detect new pathways on the CASSCF(3,3) surface which highlight the bifurcation
problem of this radical. VRIs play a role in the understanding of bifurcating reactions. The region where the bifurcation
takes place is governed by a VRI point. Because the transition state of the ring opening is not symmetric, the steepest descent
(SD) from the transition state is not along a symmetry axis either, and in this case the SD usually fails a downhill VRI point.
The SD from the transition state of the ring opening goes to the disrotatory minimum of the allyl radical. In contrast, we
find some pathways which end at the conrotatory minimum, and which go along so-called non steepest descent paths, at least
in parts. The region of interest (around the SP of the ring opening) is crossed by electronic intersection seams. Conical
intersection points on the seam can be detected by NTs. We use the possibility to explore parts of the intersection seam of
the lower CAS surface and we determine connected VRI points being the corner stones of the possible ring opening channels
in the disrotatory and the conrotatory case.
A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence
of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and
have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made
possible calculations of separate rate constants for two processes affecting the rate of phase transitionânucleation (described
with K1) and nuclei growth (described with K2). Similar phase transitions were also approximated with the well-known single constant AvramiâErofeev equation, but we successfully
calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and
explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic
curves were thus determined.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-012-9999-4
Authors
KristÄŤne KrĹŤkle-BÄrziĹa, Faculty of Chemistry, University of Latvia, Riga, Latvia
Andris ActiĹĹĄ, Faculty of Chemistry, University of Latvia, Riga, Latvia
Agris BÄrziĹĹĄ, Faculty of Chemistry, University of Latvia, Riga, Latvia
A reaction-pathway identification procedure has two distinct phases. The first phase enumerates exhaustively the feasible
candidate pathways, and the second phase identifies the ultimate feasible pathway or pathways among them. Probably the most
efficient way to execute the first phase is to algorithmically generate the networks of feasible candidate pathways from a
predefined set of plausible elementary reactions. The available algorithmic methods for this purpose can be roughly grouped
into two major classes, one based on graph theory and the other on linear algebra. Both classes of methods consider any chemical
reaction system as a network of elementary reactions, thereby implying that the two classes are interrelated. This paper studies
the linear algebraic concept termed direct mechanism introduced in the mid-eighties and the graph-theoretical concept termed
structurally minimal pathway introduced two decades later. Herein, it has been formally proven that the two concepts are equivalent.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-012-9974-0
Authors
Mate Barany, Department of Computer Science and Systems Technology, University of Pannonia, Egyetem u. 10, 8200 VeszprĂŠm, Hungary
Botond Bertok, Department of Computer Science and Systems Technology, University of Pannonia, Egyetem u. 10, 8200 VeszprĂŠm, Hungary
Csanad Imreh, Department of Computer Algorithms and Artifical Intelligence, University of Szeged, ĂrpĂĄd tĂŠr 2, 6720 Szeged, Hungary
L. T. Fan, Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506, USA
Ferenc Friedler, Department of Computer Science and Systems Technology, University of Pannonia, Egyetem u. 10, 8200 VeszprĂŠm, Hungary
For arbitrary values n and â quantum numbers, we present the solutions of the 3-dimensional SchrĂśdinger wave equation with the pseudoharmonic potential
via the SU(1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The
matrix elements r2 and
r\fracddr
are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the HellmannâFeynman
theorem, the expectation values of r2 and p2 are obtained. The energy states, the expectation values of r2 and p2 and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O2, N2, CH, H2, ScH) for arbitrary values of n and â quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature.
It is also shown that the HUP is obeyed for all diatomic molecules considered.
Content Type Journal Article
Category Review
Pages 1-21
DOI 10.1007/s10910-011-9967-4
Authors
K. J. Oyewumi, Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Kwara state, Nigeria
K. D. Sen, School of Chemistry, University of Hyderabad, Hyderabad, 50046 India
The Asymptotic Linearity Theorem (ALT), which proves the Fukui conjecture in a broader context, plays a significant role in
the repeat space theory (RST), which is the central unifying theory in the First and the Second Generation Fukui Project.
Proving the Asymptotic Linearity Theorem Extension Conjecture (ALTEC) is a fundamental problem in the repeat space theory.
The present paper constructs a class of functions MagicMtθ, which serves as a powerful tool for proving the Asymptotic Linearity Theorem Extension Conjecture and related propositions.
The d-dimensional generalization Îźd,n,θ of MagicMtθ, which is given in the present paper and is called a âd-dimensional Magic Mountainâ, provides inwardly repeating fractals in multidimensional spaces useful for interdisciplinary
research that uses the generalized repeat space theory.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-011-9963-8
Authors
Shigeru Arimoto, Division of General Education and Research, Tsuyama National College of Technology, 624-1 Numa, Tsuyama, Okayama 708-8509, Japan
In this paper, we will investigate the fuzzy layer group symmetries of two-dimensional (2D) periodic molecules. Here, we select
several graphene molecules as typical examples to discuss. For these two-dimensional graphene molecules, their MO energies,
symmetries and fuzzy symmetries are preliminarily studied. In addition, we especially make a detailed comparison between the
zigzag and armchair graphene molecules. These studies will develop a theoretical framework that will help us to investigate
the fuzzy symmetries of various layer group molecules as well as molecules with 3D periodic structure.
Content Type Journal Article
Category Original Paper
Pages 1-24
DOI 10.1007/s10910-011-9972-7
Authors
Shengkai Xing, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Yun Li, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Xuezhuang Zhao, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Zunsheng Cai, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Zhenfeng Shang, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Xiufang Xu, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Ruifang Li, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Guichang Wang, College of Chemistry, Nankai University, Tianjin, 300071 Peopleâs Republic of China
Explicit formulas for computing the ZhangâZhang polynomial of cyclo-polyphenacenes, presented by Guo et al. (J. Math. Chem.
46:347, 2009) are found to be erroneous. In the present comment, a corrected version of Theorem 4.2 is given. The new formulation has
been extensively tested by comparison with the ZhangâZhang polynomials computed by brute force using a new, completely automatized
computer code.
Content Type Journal Article
Category Letter to the Editor
Pages 1-3
DOI 10.1007/s10910-011-9969-2
Authors
Chien-Pin Chou, Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu City, 30010 Taiwan
Henryk A. Witek, Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu City, 30010 Taiwan
Garca Guirao and Lampart (J Math Chem 48:66â71, 2010; J Math Chem 48:159â164, 2010) said that for non-zero couplings constant, the lattice dynamical system is more complicated. Motivated by this, in this
paper, we prove that this coupled map lattice system is LiâYorke chaotic for coupling constant
0 < e < 1
.
Content Type Journal Article
Category Original Paper
Pages 1-5
DOI 10.1007/s10910-011-9971-8
Authors
Xinxing Wu, School of Mathematics, University of Electronic Science and Technology of China, Chengdu, 611731 Sichuan, Peopleâs Republic of China
Peiyong Zhu, School of Mathematics, University of Electronic Science and Technology of China, Chengdu, 611731 Sichuan, Peopleâs Republic of China
The theoretical model of the steady-state immobilized enzyme electrodes is discussed. This model is based on diffusion equation
containing a non-linear term related to MichaelisâMenten kinetics of the enzymatic reaction. Homotopy perturbation method
(HPM) is employed to solve the non-linear diffusion equation for the steady-state condition. Simple and approximate polynomial
expression of concentration and flux are derived for all small values of parameters
fp
(Theiele modulus) and β (kinetic parameter). Furthermore, in this work the numerical solution of the problem is also reported using SCILAB/MATLAB
program. The analytical results are compared with the numerical results and found to be in good agreement.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-011-9973-6
Authors
V. Margret PonRani, Department of Mathematics, The Madura College, Madurai, 625011 Tamilnadu, India
L. Rajendran, Department of Mathematics, The Madura College, Madurai, 625011 Tamilnadu, India
Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle
of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing
with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to
be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models
violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into
account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the
imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions
ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special
cases, both for the original models and the transformed ones.
Content Type Journal Article
Category Original Paper
Pages 1-21
DOI 10.1007/s10910-011-9961-x
Authors
Ilona Nagy, Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry J. u. 1, Budapest, 1111 Hungary
JĂĄnos TĂłth, Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry J. u. 1, Budapest, 1111 Hungary
Most nanodevices under investigation adopt a computational approach such as molecular dynamics simulations, which gives a
numerical value for the potential energy as calculated from the interaction of every atom on one molecule with every atom
on a second molecule. Although the simulation only involves short range atomâatom interactions and ignores those interactions
at longer distances, the simulation still involves significant computational time. In this paper, we determine analytical
formulae for four types of LennardâJones interactions: (i) a solid spherical nanoparticle with an atom, (ii) two distinct
radii hollow spherical fullerenes, (iii) a solid spherical nanoparticle with a hollow spherical fullerene and (iv) two distinct
radii solid spherical nanoparticles. The interaction energy using the 6â12 LennardâJones potential for these four situations
are determined using the continuum approximation, which assumes that a discrete atomic structure can be replaced by either
an average atomic surface density or an average atomic volume density. Using these formulae the computational time for a simulation
might be dramatically reduced for those molecular interactions involving spherical nanoparticles or fullerenes. Such formulae
might be exploited in hybrid analytical-computational numerical schemes, as well as in metallofullerenes and certain assumed
spherical models of molecules such as methane and ammonia. As an illustration of the formulae presented here we determine
both the most stable and the maximum radii of a solid spherical nanoparticle inside a fullerene, modelling the centre of a
carbon onion or metallofullerenes. We also determine new cut-off formulae for interacting spherical nanoparticles and fullerenes
which might be useful in computational schemes.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-011-9970-9
Authors
Richard K. F. Lee, Nanomechanics Group, School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
James M. Hill, Nanomechanics Group, School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are discussed. The analytical
expression of the kinetics of CE mechanism under first or pseudo-first order conditions with equal diffusion coefficients
at planar electrode under non-steady-state conditions are obtained by using Homotopy perturbation method. These simple new
approximate expressions are valid for all values of time and possible values of rate constants. Analytical equations are given
to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working
surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant.
In this work we employ the Homotopy perturbation method to solve the boundary value problem. Furthermore, in this work the
numerical simulation of the problem is also reported using Scilab program. The analytical results are found to be in excellent
agreement with the numerical results.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-011-9968-3
Authors
K. Indira, Department of Mathematics, The Madura College, Madurai, 625011 India
L. Rajendran, Department of Mathematics, The Madura College, Madurai, 625011 India
In this paper we study the connection between: (i) closed Newton-Cotes formulae of high order, (ii) trigonometrically-fitted
and exponentially-fitted differential methods, (iii) symplectic integrators. Several one step symplectic integrators have
been produced based on symplectic geometry during the last decades (see the relevant literature and the references here).
However, the study of multistep symplectic integrators is very poor. In this paper we investigate the High Order Closed Newton-Cotes
Formulae and we write them as symplectic multilayer structures. We develop trigonometrically-fitted and exponentially-fitted
symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes in order to solve
the resonance problem of the radial SchrĂśdinger equation. Based on the theoretical and numerical results, conclusions on the
efficiency of the new obtained methods are given.
Content Type Journal Article
Category Original Paper
Pages 1-38
DOI 10.1007/s10910-011-9965-6
Authors
T. E. Simos, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451 Saudi Arabia
In this project we evaluate second virial coefficient of some inert gases via classical cluster expansion, assuming each atomic
pair interaction is of Lennard-Jones type. We also try to numerically evaluate the third virial coefficient of Argon gas based
on bipolar-coordinate integration (Mas et al. in J Chem Phys 10:6694, 1999), assuming the same Lennard-Jones potential as before. The second virial coefficient (Vega et al. in Phys Chem Chem Phys
4:3000â3007, 2002) calculated from our model are compatible to the experimental data [19] The temperature at which B2(T) â 0 is called the Boyleâs temperature TB (Vega et al. in Phys Chem Chem Phys 4:3000â3007, 2002) for the Lennard-Jines (12-6) potential. For the second virial coefficient of He, we obtain the Boyleâs temperature as follow:
TB = 34.9312438964844 (K) B2(T) = 9.82958 Ă 10â6 (cm3/mol).
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-011-9966-5
Authors
Artit Hutem, Forum for Theoretical and Computational Physics, Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
Sutee Boonchui, Forum for Theoretical and Computational Physics, Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller
circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K2, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing
of HC(n) with P6 and K1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-011-9962-9
Authors
Indra Rajasingh, Department of Mathematics, Loyola College, Chennai, 600 034 India
Albert Muthumalai, Department of Mathematics, Loyola College, Chennai, 600 034 India
R. Bharati, Department of Mathematics, Loyola College, Chennai, 600 034 India
A. S. Shanthi, Department of Mathematics, Loyola College, Chennai, 600 034 India
Shifting the origin of a known quantum object set (QOS) or of some discrete molecular point cloud (MPC) by choosing the centroid
of such sets, leads to the way to produce quantum similarity matrices (SM) and tensors, which can be systematically referred to a canonical origin, whatever their nature, dimension or cardinality. In this paper the source, significance and properties of such centroid
origin shift and the characteristics of the resultant shifted SM are discussed in deep. From such an analysis some interesting
applications emerge; as, for instance, a new collection of MPC ordering possibilities. In addition, although all the procedures
in this work are described by means of a quantum similarity theoretical background, based on QOS structure within the space
of molecules, everything can be also easily implemented in a classical QSPR framework made of molecular numerical images attached
to discrete molecular vectors, constructed with well-defined descriptor parameters.
Content Type Journal Article
Category Original Paper
Pages 1-18
DOI 10.1007/s10910-011-9960-y
Authors
Ramon CarbĂł-Dorca, Institute of Computational Chemistry, University of Girona, Girona, 17071 Catalonia, Spain
Emili BesalĂş, Institute of Computational Chemistry, University of Girona, Girona, 17071 Catalonia, Spain
It is well known that oscillations in models of biochemical reaction networks can arise as a result of a single negative cycle.
On the other hand, methods for finding general network conditions for potential oscillations in large biochemical reaction
networks containing many cycles are not well developed. A biochemical reaction network with any number of species is represented
by a simple digraph and is modeled by an ordinary differential equation (ODE) system with non-mass action kinetics. The obtained
graph-theoretic condition generalizes the negative cycle condition for oscillations in ODE models to the existence of a pair
of subnetworks, where each subnetwork contains an even number of positive cycles. The technique is illustrated with a model
of genetic regulation.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-011-9955-8
Authors
Maya Mincheva, Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
A power-series potential energy function that is analogous to that of the Molski potential is proposed herein such that reductions
to the Dunham and Simons-Parr-Finlan (SPF) potential functions are obtained by prescribing numerical values of 0 and 1 respectively
to a type parameter. The type parameter takes the form of an index instead of a multiplier in the case of the Molski potential.
Verification of the proposed potential function was performed by comparing it alongside the Dunham, SPF and Ogilvie potentials
in being fitted to the RKR results of CO diatomic molecule. The proposed potential with the selection of central value to
its type parameter is a geometric mean analogy to the Ogilvie potentialâs arithmetic mean of the Dunham and SPF potential
functions. Although prescription of any numerical value to the type parameter allows good curve fit within the range of RKR
data, the extent of convergence is influenced by the choice of type parameter. Having shown the validity of the proposed potential,
further studies is proposed in order to establish the comparative advantages of this potential with other power-series potential
energy function.
Content Type Journal Article
Category Original Paper
Pages 1-9
DOI 10.1007/s10910-011-9952-y
Authors
Teik-Cheng Lim, School of Science and Technology, SIM University, 461 Clementi Road, Singapore, 599491 Singapore
Spherical harmonics in an arbitrary dimension are employed widely in quantum theory. Spherical harmonics are also called hyperspherical
harmonics when the dimension is larger than 3. In this paper, we derive some integral identities involving spherical harmonics
in an arbitrary dimension.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-011-9956-7
Authors
Weimin Han, Department of Mathematics and Program in Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA 52242, USA
Kendall Atkinson, Department of Computer Science and Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Hao Zheng, Department of Chemistry, Zhejiang University, Hangzhou, 310027 China
Factorization formulas are used to derive a uniform semiclassical approximation of transition probabilities. The latter are
determined in the analytical form where the basis transition probabilities are set by the analytical formula. As an example,
we consider the rigid rotor, harmonic oscillator, and Morse oscillator in collisions with structureless particles.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-011-9958-5
Authors
M. L. Strekalov, Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Theoretical Chemistry Laboratory, 3 Institutskaya Street, 630090 Novosibirsk, Russia
In this paper we expand the equations governing MichaelisâMenten kinetics in a total quasi-steady state setting, finding the
first order uniform expansions. Our results improve previous approximations and work well especially in presence of an enzyme
excess.
Content Type Journal Article
Category Original Paper
Pages 1-13
DOI 10.1007/s10910-011-9957-6
Authors
Guido DellâAcqua, Dipartimento di Scienze di Base e Applicate per lâIngegneria (S.B.A.I.), âSapienzaâ University, Via A. Scarpa 16, 00161 Rome, Italy
Alberto Maria Bersani, Dipartimento di Scienze di Base e Applicate per lâIngegneria (S.B.A.I.), âSapienzaâ University, Via A. Scarpa 16, 00161 Rome, Italy
We report on a comparison of the diffraction pattern observed for nanocrystalline n-diamond and i-carbon forms by other investigative
teams, with the calculated diffraction pattern of glitter based upon lattice parameters optimized using the DFT-CASTEP method.
The close fit of the latter dataset to that observed for n-diamond and i-carbon, as reported herein, suggests that indeed
i-carbon may be of the same structure as n-diamond, and that they both may have the tetragonal glitter structure.
Content Type Journal Article
Category Brief Communication
Pages 1-5
DOI 10.1007/s10910-011-9954-9
Authors
Michael J. Bucknum, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Buenos Aires, Republic of Argentina
Eduardo A. Castro, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Buenos Aires, Republic of Argentina
Collisional energy transfer between highly vibrationally excited molecules and a bath gas is considered as a stochastic process
occurring in energy space. An exact solution to master equation for the conditional probability is given in terms of simple
analytical formulas for weak and strong collisions. The strong collisions are shown to manifest themselves in the distribution
pattern composed of maxima and minima in the energy dependence of conditional probability. This effect is explained in detail
on physical grounds.
Content Type Journal Article
Category Letter to the Editor
Pages 1-10
DOI 10.1007/s10910-011-9951-z
Authors
M. L. Strekalov, Theoretical Chemistry Laboratory, Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, 3 Institutskaya Street, 630090 Novosibirsk, Russia
