We present a refinement of recently proposed characterization of molecules based on a sequence of powers of interatomic separations referred to as molecular profiles. The molecular profiles and closely related shape p...
We present a refinement of recently proposed characterization of molecules based on a sequence of powers of interatomic separations referred to as molecular profiles. The molecular profiles and closely related shape profiles were based on the averaging contributions arising from different powers of interatomic distances for atoms in a molecule or atoms at the molecular periphery, respectively. Consequently, molecular models in which atoms have the same set of coordinates but different bonding patterns will result in identical molecular profiles. In this article we outline a refinement of molecular profiles in which the bonding pattern in a molecule is fully acknowledged. This is accomplished by adding ''ghost'' sites along chemical bonds. The distance-based invariants of the augmented matrix reflect the bonding pattern of a structure giving different molecular profiles for molecules having the same atomic coordinates but different bondings. The procedure is general and applies to two-dimensional and three-dimensional molecular skeletons. Equally, the approach can be applied to van der Waals-type molecular surfaces and molecular contours of equal electron densities in order to obtain characterization of more realistic molecular models.
The significance of the existing analysis methods in complex networks and easy access to the ever-increasing volume of information present the emergence of proposing new methods in various fields based on complex syst...
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The significance of the existing analysis methods in complex networks and easy access to the ever-increasing volume of information present the emergence of proposing new methods in various fields based on complex system ideas. However, these systems are usually faced with various random failures and intelligent attacks. Due to the nature of the components’ behaviors, the occurrence of the failures and faults in their operations and the alteration of their topologies are the most important problems. Since the complex systems are usually used as the infrastructures of other networks, their robustness against failures and the adoption of suitable precautions are necessary. Moreover, the smallworld effect in most complex systems is one of the crucial structural features. The authors found that the relation between these two is not well-known and may even be in conflict in some networks. The main goal in this paper is to achieve an optimal topology by utilizing a robustness-oriented multiobjective trade-off optimization model(edge rewiring) to establish a peaceful relationship between the two requirements. By offering a proposed rewiring method with the small-world effect, which is called core-periphery Windmill property, the authors demonstrated that the generated networks are able to exhibit appropriate robustness even during intelligent attacks. The results obtained in terms of Windmill graphs are presented very good approximations to demonstrate the small-world effect. These graphs are used as the initial core in the construction of the optimized networks’ topologies.
Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures....
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Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures. Moreover, a complete classification of isoparametric families in a Funk space is given.
The Hilfer fractional derivative interpolates the commonly used Riemann-Liouville and Caputo fractional derivative. In general, solutions to Hilfer fractional differential equations are singular for t ↓ 0 and are dif...
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It is frequently argued that reality and locality are incompatible with the predictions of quantum mechanics. Various investigators have used this as evidence for the existence of hidden variables. However, Bell's...
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It is frequently argued that reality and locality are incompatible with the predictions of quantum mechanics. Various investigators have used this as evidence for the existence of hidden variables. However, Bell's inequalities seem to refute this possibility. Since the above arguments are made within the framework of conventional probability theory, we contend that an alternative solution can be found by an extension of this theory. Elaborating on some ideas of I. Pitowski, we show that within the framework of a generalized probability theory, reality, locality, hidden variables, and the predictions of quantum mechanics can be maintained together. Although our principal model in this work is a spin system, there are indications that this program can be extended to more general systems.
Let L be a uniformly parabolic linear partial differential operator. We show that nonnegative solutions of the differential inequality Lu less-than-or-equal-to c(u + \NABLA u\) on R(n) x (O, T) for which u(x, T) = 0(e...
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Let L be a uniformly parabolic linear partial differential operator. We show that nonnegative solutions of the differential inequality Lu less-than-or-equal-to c(u + \NABLA u\) on R(n) x (O, T) for which u(x, T) = 0(exp(-delta\x\2)) must be identically zero if the constant delta is sufficiently large. An analogous result is given for nonlinear systems.
A description of quarks is given in terms of a finite-dimensional Hilbert space model. Color and flavor observables are defined and the corresponding motion and energy observables are constructed using the methods of ...
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A description of quarks is given in terms of a finite-dimensional Hilbert space model. Color and flavor observables are defined and the corresponding motion and energy observables are constructed using the methods of finite-dimensional quantum mechanics. It is shown that a fundamental color condition implies that quarks can only combine as mesons, baryons, antibaryons, and collections of these. Baryon and meson Hamiltonians are proposed and various masses are computed.
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