On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

A Periodic Lotka-Volterra System

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.

Mean-Periodic Solutions of Retarded Functional Differential Equations

In this paper we present a spectral criterion for existence of mean-periodic solutions of retarded functional differential equations with a time-independent main part.

Algorithm BIDIMS for Automated Systematization of Data Array. Case Study: Rediscovering Mendeleev’s Periodic Table of Chemical Elements

The method (algorithm BIDIMS) of multivariate objects display to bidimensional structure in which the sum of differences of objects properties and their nearest neighbors is minimal is being described. The basic regularities on the set of objects at this ordering become evident. Besides, such structures (tables) have high inductive opportunities: many latent properties of objects may be predicted on their coordinates in this table. Opportunities of a method are illustrated on an example of bidimentional ordering of chemical elements. The table received in result practically coincides with the periodic Mendeleev table.

Localized waves in optical systems with periodic dispersion and nonlinearity management

We overview our recent developments in the theory of dispersion-managed (DM) solitons within the context of optical applications. First, we present a class of localized solutions with a period multiple to that of the standard DM soliton in the nonlinear Schrödinger equation with periodic variations of the dispersion. In the framework of a reduced ordinary differential equation-based model, we discuss the key features of these structures, such as a smaller energy compared to traditional DM solitons with the same temporal width. Next, we present new results on dissipative DM solitons, which occur in the context of mode-locked lasers. By means of numerical simulations and a reduced variational model of the complex Ginzburg-Landau equation, we analyze the influence of the different dissipative processes that take place in a laser.

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

Search for Wieferich Primes through the use of Periodic Binary Strings

The result of the distributed computing projectWieferich@Home is presented: the binary periodic numbers of bit pseudo-length j ≤ 3500 obtained by replication of a bit string of bit pseudo-length k ≤ 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Surface plasmon resonance-induced photocatalysis by Au nanoparticles decorated mesoporous g-C3N4 nanosheets under direct sunlight irradiation

In recent years, surface plasmon-induced photocatalytic materials with tunable mesoporous framework have attracted considerable attention in energy conversion and environmental remediation. Herein we report a novel Au nanoparticles decorated mesoporous graphitic carbon nitride (Au/mp-g-C3N4) nanosheets via a template-free and green in situ photo-reduction method. The synthesized Au/mp-g-C3N4 nanosheets exhibit a strong absorption edge in visible and near-IR region owing to the surface plasmon resonance effect of Au nanoparticles. More attractively, Au/mp-g-C3N4 exhibited much higher photocatalytic activity than that of pure mesoporous and bulk g-C3N4 for the degradation of rhodamine B under sunlight irradiation. Furthermore, the photocurrent and photoluminescence studies demonstrated that the deposition of Au nanoparticles on the surface of mesoporous g-C3N4 could effectively inhibit the recombination of photogenerated charge carriers leading to the enhanced photocatalytic activity. More importantly, the synthesized Au/mp-g-C3N4 nanosheets possess high reusability. Hence, Au/mp-g-C3N4 could be promising photoactive material for energy and environmental applications.

Mesoporous sulfonic acid silicas for pyrolysis bio-oil upgrading via acetic acid esterification

Propylsulfonic acid derivatised SBA-15 catalysts have been prepared by post modification of SBA-15 with mercaptopropyltrimethoxysilane (MPTMS) for the upgrading of a model pyrolysis bio-oil via acetic acid esterification with benzyl alcohol in toluene. Acetic acid conversion and the rate of benzyl acetate production was proportional to the PrSO3H surface coverage, reaching a maximum for a saturation adlayer. Turnover frequencies for esterification increase with sulfonic acid surface density, suggesting a cooperative effect of adjacent PrSO3H groups. Maximal acetic acid conversion was attained under acid-rich conditions with aromatic alcohols, outperforming Amberlyst or USY zeolites, with additional excellent water tolerance.

Hierarchical mesoporous Pd/ZSM-5 for the selective catalytic hydrodeoxygenation of m-cresol to methylcyclohexane

Mesopore incorporation into ZSM-5 enhances the dispersion of Pd nanoparticles throughout the hierarchical framework, significantly accelerating m-cresol conversion relative to a conventional microporous ZSM-5, and dramatically increasing selectivity towards the desired methylcyclohexane deoxygenated product. Increasing the acid site density further promotes m-cresol conversion and methylcyclohexane selectivity through efficient dehydration of the intermediate methylcyclohexanol.