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In this paper, we investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case, we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities. [ABSTRACT FROM AUTHOR]

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker–Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such nonstandard models by reformulating and extending the classical entropy method, under the assumption of periodic boundary condition. In addition, illustrative numerical tests are presented to highlight the essential points of the current analytical results and to motivate future analysis. [ABSTRACT FROM AUTHOR]

In this paper, by using the Yukawa coupling mechanism, we consider the fermion localization in two types of braneworld models driven by real scalar fields with non-standard dynamics. Because of the existing freedom in the form of the Yukawa coupling, we consider two coupling forms between the background scalar field and spinors where one is arising from the geometry shape of the warp factor and the other is a function of the background scalar field containing a derivative scalar-fermion coupling. With two coupling functions, it is shown that the massless zero mode of fermion fields is localized on both branes with generalized dynamic depending on the values of the coupling constants. However, there is no localized mode when the Yukawa coupling only contains a derivative term of the background scalar field. Furthermore, effects of the parameters of the models on the zero mode and fermion effective potential are addressed. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results. [ABSTRACT FROM AUTHOR]

We investigate the nonstandard neutrino interactions (NSI) in the rare decays of B c + mesons involving neutrinos in the final state. It is suggested that the interference between Standard Model and nonstandard interaction can provide sizeable contribution. We calculate the limits on NSI free parameters ( 𝜖 τ τ u L , 𝜖 τ τ d L ) and compare them with experimental data. [ABSTRACT FROM AUTHOR]

Let be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope. [ABSTRACT FROM AUTHOR]

Alternate quadratic systems where and are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram ('hidden' because it is not visible at normal resolution and 'nonstandard' because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A. [ABSTRACT FROM AUTHOR]

Generalized Dirac equation with operator mass term is presented. Its solutions are nonstandard spinors (NSS) which, like eigenspinoren des Ladungskonjugationsoperators (ELKO), are eigenvectors of the charge conjugation and dual-helicity operators. It is demonstrated that in spite of their noncovariant nature the NSS can serve as a carrier space of a representation of Poincaré group. However, the corresponding boost generators are not manifestly covariant and generate nonlocal momentum dependent transformations, which are presented explicitly. These results can present a new look on group-theoretical grounds of ELKO theories. [ABSTRACT FROM AUTHOR]

A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomol'nyi equations. The Bogomol'nyi-Prasad-Sommerfield (BPS) energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The self-dual equations are solved analytically and verified numerically. [ABSTRACT FROM AUTHOR]

In this paper, we present two real-world situations in which the standard hypotheses of a bargaining problem do not hold, and discuss how to tackle these situations. [ABSTRACT FROM AUTHOR]

We prove a nonstandard central limit theorem for strongly mixing stationary sequences using the "radically elementary" probability theory developed by Nelson (1987) and use this result to obtain a nonstandard Markov chain central limit theorem. An analogue of a Gaussian autoregressive process is used to illustrate how to obtain the rate of convergence. A Markov chain nonstandard functional central limit theorem is also proved under conditions similar to square integrability of the underlying martingale. [ABSTRACT FROM AUTHOR]

In this paper, we study some periodicity concepts on words. First, we extend the notion of full tilings which was recently introduced by Karhumäki, Lifshits, and Rytter to partial tilings. Second, we investigate the notion of quasiperiods and show in particular that the set of quasiperiodic words is a context-sensitive language that is not context-free, answering a conjecture by Dömösi, Horváth and Ito. [ABSTRACT FROM AUTHOR]

We consider a model of margin trading based on the hyperfinite timeline. Using only elementary nonstandard analysis we are able to derive explicit formulas for the expected margin call time and loss. Further margin trading strategy is studied and an application to pricing barrier option is given. We prove a generalization of the Catalan numbers which forms the combinatoric basis of our results and should be of independent interest. [ABSTRACT FROM AUTHOR]

The paradox of the Stop-Loss-Start-Gain trading strategy is resolved by showing that along the hyperfinite timeline the strategy incurs infinitesimal losses summing up to a non-infinitesimal amount. As a consequence, the Black–Scholes formula is derived using only hyperreal arithmetic and Riemann sum, probably the most elementary derivation thus far. [ABSTRACT FROM AUTHOR]

In this paper, an alternative proof is presented of the following result on symbolic powers due to Ein, Lazarsfeld and Smith [3] (for the affine case over C) and to Hochster and Huneke [4] (for the general case). Let A be a regular ring containing a field K. Let a be a radical ideal of A and let h be the maximum of the heights of its minimal primes. Then for all n, we have an inclusion a[SUP(hn)] ⊂ a[SUPn], where the first ideal denotes the hnth symbolic power of a. In prime characteristic, this result admits an easy tight closure proof due to Hochster and Huneke. In this paper, the characteristic zero version is obtained from this by an application of the Lefschetz Principle. [ABSTRACT FROM AUTHOR]

Kelemen and Robinson reconstructed the [formula] model of Glimm and Jaffe with methods of nonstandard analysis. In order to apply nonstandard analysis to other constructions of field models systematically, this paper generalizes their nonstandard analytical methods of representing the canonical commutation relations in the framework of the theory of nonstandard unitary representations. For this purpose, such notions are introduced and examined in detail as nonstandard hulls of representations, approximate representations, and their standardizations. As applications, the following representations are reconstructed in this framework: the Segal representation, relativistic time zero fields, and the Araki–Woods representation. [formula available in full text]. [ABSTRACT FROM AUTHOR]

Nonstandard finite difference schemes offer the potential for either constructing exact discrete models of differential equations or obtaining discrete models that do not have the elementary numerical instabilities. While the general laws for constructing such schemes are not precisely known at the present time, a number of important rules have been discovered. This paper provides an introduction to the nonstandard finite difference rules, explains their significance, and applies them to several model ordinary and partial differential equations. Several major unresolved issues and problems are briefly discussed. [ABSTRACT FROM AUTHOR]