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Reentrant Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in the honeycomb latticeOct 17 2017May 29 2018We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field ... More

The influence of magnetic field on the superconducting properties and the BCS-BEC crossover in systems with local fermion pairingSep 25 2013The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to ... More

On the Imbalanced d-wave Superfluids within the Spin Polarized Extended Hubbard Model: Weak Coupling LimitSep 25 2013We investigate the superfluid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic field. We analyze the temperature and magnetic field dependencies of the order parameter. We find that in the two-dimensional case, ... More

On the BCS-BEC crossover in the Spin-Polarized Attractive Hubbard Model at T=0Sep 25 2013The influence of the Zeeman magnetic field ($h$) on the ground state evolution of superfluid properties from the weak coupling (BCS like) to the strong coupling limit of tightly bound local pairs (LP) with increasing attraction has been studied. The analysis ... More

Orbital magnetism of ultracold fermionic gases in a lattice: dynamical mean-field approachFeb 25 2016May 29 2016We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling term. Our main ... More

On the BCS-BEC crossover in the 2D Asymmetric Attractive Hubbard ModelSep 25 2013We analyze the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) in the 2D asymmetric attractive Hubbard model, in the presence of the Zeeman magnetic field ($h$). The broken symmetry Hartree ... More

Lattice Hamiltonian approach to the massless Schwinger model: precise extraction of the mass gapNov 27 2012Feb 12 2013We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. ... More

Lattice Hamiltonian approach to the Schwinger model: further results from the strong coupling expansionOct 28 2014Oct 29 2014We employ exact diagonalization with strong coupling expansion to the massless and massive Schwinger model. New results are presented for the ground state energy and scalar mass gap in the massless model, which improve the precision to nearly $10^{-9} ... More

Stability of superfluid phases in the 2D Spin-Polarized Attractive Hubbard ModelSep 25 2013We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) with increasing attraction, in the presence of the Zeeman magnetic field ($h$) for $d=2$, within the spin-polarized attractive ... More

Phase separations induced by a trapping potential in one-dimensional fermionic systems as a source of core-shell structuresMar 19 2019Ultracold fermionic gases in optical lattices give a great opportunity for creating different types of novel states. One of them is phase separation induced by a trapping potential between different types of superfluid phases. The core-shell structures, ... More

Suppression and revival of long-range ferromagnetic order in the multiorbital Fermi-Hubbard modelFeb 08 2018By means of dynamical mean-field theory allowing for complete account of SU(2) rotational symmetry of interactions between spin-1/2 particles, we observe a strong effect of suppression of ferromagnetic order in the multiorbital Fermi-Hubbard model in ... More

Quantum engineering of Majorana quasiparticles in one-dimensional optical latticesJun 13 2017We propose a feasible way of engineering Majorana-type quasiparticles in ultracold fermionic gases on a one-dimensional (1D) optical lattice. For this purpose, imbalanced ultracold atoms interacting by the spin-orbit coupling should be hybridized with ... More

A comparison of the cut-off effects for Twisted Mass, Overlap and Creutz fermions at tree-level of Perturbation TheoryNov 04 2008In this paper we investigate the cutoff effects at tree-level of perturbation theory for three different lattice regularizations of fermions -- maximally twisted mass Wilson, overlap and Creutz fermions. We show that all three kinds of fermions exhibit ... More

Suppression and revival of long-range ferromagnetic order in the multiorbital Fermi-Hubbard modelFeb 08 2018Jun 29 2018By means of dynamical mean-field theory allowing for complete account of SU(2) rotational symmetry of interactions between spin-1/2 particles, we observe a strong effect of suppression of ferromagnetic order in the multiorbital Fermi-Hubbard model in ... More

Quark mass anomalous dimension and $Λ_{\overline{\textrm{MS}}}$ from the twisted mass Dirac operator spectrumNov 14 2013Jul 29 2014We investigate whether it is possible to extract the quark mass anomalous dimension and its scale dependence from the spectrum of the twisted mass Dirac operator in Lattice QCD. The answer to this question appears to be positive, provided that one goes ... More

Phase transitions in quasi-one dimensional system with unconventional superconductivityOct 04 2017The paper is devoted to a study of superconducting properties of population-imbalanced fermionic mixtures in quasi-one dimensional optical lattices. The system can be effectively described by the attractive Hubbard model with the Zeeman magnetic field ... More

Critical behaviour in one dimension: unconventional pairing, phase separation, BEC-BCS crossover and magnetic Lifshitz transitionFeb 07 2017We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional (1D) optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic ... More

Application of Contractor Renormalization Group (CORE) to the Heisenberg zig-zag and the Hubbard chainMay 14 2008The COntractor REnormalization group method was devised in 1994 by Morningstar and Weinstein. It was primarily aimed at extracting the physics of lattice quantum field theories (like lattice Quantum Chromodynamics). However, it is a general method of ... More

Hardy spaces for the Dunkl harmonic oscillatorFeb 23 2018Apr 14 2018Let $\Delta$ and $L=\Delta -\|\mathbf x\|^2$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $\mathcal H^1$ associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with ... More

Misiurewicz parameters for Weierstrass elliptic functions based on triangle and square latticesDec 23 2013For two families of Weierstrass elliptic functions - based on triangular or square lattices - we prove that the set of Misiurewicz parameters has the Lebesgue measure zero in C.

DG categories and exceptional collectionsMay 28 2012Jan 21 2013Bondal and Kapranov describe how to assign to a full exceptional collection on a variety X a DG category C such that the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of C. In this paper we show that the ... More

No entire function with real multipliers in class SJul 18 2012We prove that there is no entire transcendental function in class S with real multipliers of all repelling periodic orbits.

DG quivers of smooth rational surfacesJan 27 2013Let X be a smooth rational surface. We calculate a DG quiver of a full exceptional collection of line bundles on X obtained by an augmentation from a strong exceptional collection on the minimal model of X. In particular, we calculate canonical DG algebras ... More

$N_f = 2+1+1$ flavours of twisted mass quarks: cut-off effects at tree-level of perturbation theoryDec 22 2010Jan 30 2011We present a calculation of cut-off effects at tree-level of perturbation theory for the K and D mesons using the twisted mass formulation of lattice QCD. The analytical calculations are performed in the time-momentum frame. The relative sizes of cut-off ... More

Optimal upper bounds on expected kth record values from IGFR distributionsFeb 04 2019The paper concerns the optimal upper bounds on the expectations of the kth record values (k >= 1) centered about the sample mean. We consider the case, when the records are based on the infinite sequence of the independent identically distributed random ... More

Hardy spaces for the Dunkl harmonic oscillatorFeb 23 2018May 13 2019Let $\Delta$ and $L=\Delta -\|\mathbf x\|^2$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $\mathcal H^1$ associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with ... More

Magnetic Lifshitz transition and its consequences in multi-band iron-based superconductorsFeb 08 2017In this paper we address Lifshitz transition induced by applied external magnetic field in a case of iron-based superconductors, in which a difference between the Fermi level and the edges of the bands is relatively small. We introduce and investigate ... More

Topological susceptibility from the twisted mass Dirac operator spectrumDec 18 2013Mar 31 2014We present results of our computation of the topological susceptibility with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization ... More

Chiral condensate from the twisted mass Dirac operator spectrumMar 08 2013Oct 14 2013We present the results of our computation of the chiral condensate with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions. The condensate is determined from the Dirac operator spectrum, applying the spectral projector method proposed ... More

Twisted mass Dirac spectrumDec 05 2016The microscopic spectral density for lattice QCD with $N_f = 2+1+1$ twisted mass fermions is computed numerically and compared to analytical predictions of Wilson $\chi$-PT at a fixed index. In this way, we obtain results for the chiral condensate and ... More

Continuum-limit scaling of overlap fermions as valence quarksOct 05 2009We present the results of a mixed action approach, employing dynamical twisted mass fermions in the sea sector and overlap valence fermions, with the aim of testing the continuum limit scaling behaviour of physical quantities, taking the pion decay constant ... More

Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge actionJul 03 2012We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour ... More

Step scaling in coordinate space: running of the quark massOct 25 2016We perform a benchmark study of the step scaling procedure for the ratios of renormalization constants extracted from position space correlation functions. We work in the quenched approximation and consider the pseudoscalar, scalar, vector and axial vector ... More

Non-perturbative running of renormalization constants from correlators in coordinate space using step scalingAug 08 2016Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell ... More

The continuum limit of the $D$ meson, $D_s$ meson and charmonium spectrum from $N_f=2+1+1$ twisted mass lattice QCDMar 21 2016We compute masses of $D$ meson, $D_s$ meson and charmonium states using $N_f=2+1+1$ Wilson twisted mass lattice QCD. All results are extrapolated to physical light quark masses, physical strange and charm quark masses and to the continuum. Our analysis ... More

Continuum Limit of Overlap Valence Quarks on a Twisted Mass SeaDec 20 2010We study a lattice QCD mixed action with overlap valence quarks on two flavours of Wilson maximally twisted mass sea quarks. Employing three different matching conditions to relate both actions to each other, we investigate the continuum limit by using ... More

Continuum limit of the $D$ meson, $D_s$ meson and charmonium spectrum from $N_f=2+1+1$ twisted mass lattice QCDMar 21 2016Nov 22 2016We compute masses of $D$ meson, $D_s$ meson and charmonium states using $N_f=2+1+1$ Wilson twisted mass lattice QCD. All results are extrapolated to physical light quark masses, physical strange and charm quark masses and to the continuum. Our analysis ... More

Short distance singularities and automatic O($a$) improvement: the cases of the chiral condensate and the topological susceptibilityDec 01 2014Apr 13 2015Short-distance singularities in lattice correlators can modify their Symanzik expansion by leading to additional O($a$) lattice artifacts. At the example of the chiral condensate and the topological susceptibility, we show how to account for these lattice ... More

The Ramsey number for a triple of large cyclesSep 01 2007We find the asymptotic value of the Ramsey number for a triple of long cycles, where the lengths of the cycles are large but may have different parity.

Anomalous diffusion models: different types of subordinator distributionOct 13 2011Subordinated processes play an important role in modeling anomalous diffusion-type behavior. In such models the observed constant time periods are described by the subordinator distribution. Therefore, on the basis of the observed time series, it is possible ... More

Self-Regulation in Infinite Populations with Fission-Death DynamicsJul 11 2018The evolution of an infinite population of interacting point entities placed in $\mathbb{R}^d$ is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The ... More

Style transfer-based image synthesis as an efficient regularization technique in deep learningMay 27 2019These days deep learning is the fastest-growing area in the field of Machine Learning. Convolutional Neural Networks are currently the main tool used for image analysis and classification purposes. Although great achievements and perspectives, deep neural ... More

Topological expansion of the coefficients of zonal polynomials in genus oneAug 16 2011We use a combinatorial interpretation of the coefficients of zonal Kerov polynomials as a number of unoriented maps to derive an explicit formula for the coefficients in genus one.

On some nonlinear extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear eigenvalue problemsApr 11 2011We derive inequality [\int_{\r} |f^{'}(x)|^ph(f(x))dx \le (\sqrt{p-1})^p\int_{\r}(\sqrt{|f^{"}(x){\cal T}_h(f(x))|})^ph(f(x))dx,] where $f$ belongs locally to Sobolev space $W^{2,1}$ and $f^{'}$ has bounded support. Here $h(...)$ is a given function and ... More

Evolution of states of an infinite fission-death systemApr 04 2018The evolution of an infinite system of interacting point entities with traits $x\in \mathds{R}^d$ is studied. The elementary acts of the evolution are state-dependent death of an entity with rate that includes a competition term and independent fission ... More

On weak Sierpiński sets in groups and free subgroupsMay 29 2018Mar 19 2019In this paper we discuss the problem of existence of so called weak Sierpi\'nski sets in groups. It is known that group $G$ has a Sierpi\'nski subset if and only if it contains a free subgroup. In their paper, Tomkowicz and Wagon conjectured that an analogous ... More

Compressed sensing for real measurements of quaternion signalsMay 25 2016The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear measurements, provided ... More

Nonlinear parabolic problems in Musielak--Orlicz spacesJun 10 2013Our studies are directed to the existence of weak solutions to a parabolic problem containing a multi-valued term. The problem is formulated in the language of maximal monotone graphs. We assume that the growth and coercivity conditions of a nonlinear ... More

Dipole model analysis of highest precision HERA data, including very low $Q^2$'sNov 30 2016We analyse, within a dipole model, the final, inclusive HERA DIS cross section data in the low $x$ region, using fully correlated errors. We show, that these highest precision data are very well described within the dipole model framework starting from ... More

Microsimulations of demographic changes in England and Wales under various EU referendum scenariosJun 15 2016Jun 24 2016We perform stochastic microsimulations of the dynamics of England and Wales's population after the British referendum on EU membership. Employing the available survey data, we model and predict the demographics of the next generation, as shaped by international ... More

Cross-sectional Markov model for trend analysis of observed discrete distributions of population characteristicsOct 22 2015We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the practical problems ... More

On weak Sierpiński sets in groups and free subgroupsMay 29 2018Jul 12 2018In this paper we discuss the problem of existence of so called weak Sierpi\'nski sets in groups. It is known that group $G$ has a Sierpi\'nski subset if and only if it contains a free subgroup. In their paper, Tomkowicz and Wagon conjectured that an analogous ... More

Remark on atomic decompositions for Hardy space $H^1$ in the rational Dunkl settingMar 27 2018Mar 23 2019Let $\Delta$ be the Dunkl Laplacian on $\mathbb R^N$ associated with a normalized root system $R$ and a multiplicity function $k(\alpha)\geq 0$. We say that a function $f$ belongs to the Hardy space $H^1_{\Delta}$ if the nontangential maximal function ... More

Kummer and gamma laws through independences on trees - another parallel with the Matsumoto-Yor propertyOct 31 2015Jul 14 2016The paper develops a rather unexpected parallel to the multivariate Matsumoto--Yor (MY) property on trees considered in \cite{MW04}. The parallel concerns a multivariate version of the Kummer distribution, which is generated by a tree. Given a tree of ... More

Compressed sensing in the quaternion algebraApr 25 2017May 22 2017The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$-norm minimization - a sparse quaternion signal from a limited number of its linear measurements, provided the ... More

The (Non-)Utility of Structural Features in BiLSTM-based Dependency ParsersMay 29 2019Jun 04 2019Classical non-neural dependency parsers put considerable effort on the design of feature functions. Especially, they benefit from information coming from structural features, such as features drawn from neighboring tokens in the dependency tree. In contrast, ... More

Ringel duality as an instance of Koszul dualityJan 22 2017Dec 19 2017In their previous work, S. Koenig, S. Ovsienko and the second author showed that every quasi-hereditary algebra is Morita equivalent to the right algebra, i.e. the opposite algebra of the left dual, of a coring. Let $A$ be an associative algebra and $V$ ... More

Anisotropic parabolic problems with slowly or rapidly growing termsJul 09 2013Nov 26 2013We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued with growth conditions formulated with help of an $x-$dependent $N-$function. The main novelty of the paper consists in the lack of any growth restrictions ... More

On one variant of strongly nonlinear Gagliardo-Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problemsNov 06 2018We obtain the inequality $$\int_{\Omega}|\nabla u(x)|^ph(u(x))dx\leq C(n,p)\int_{\Omega} \left( \sqrt{ |\Delta u(x)||{\cal T}_{h,C}(u(x))|}\right)^{p}h(u(x))dx,$$ where $\Omega\subset \mathbf{R}^n$ is a bounded Lipschitz domain, $u\in W^{2,1}_{loc}(\Omega)$ ... More

On certain variant of strongly nonlinear interpolation inequality in dimension nNov 26 2016We obtain the inequality $$\int_{\Omega}|\nabla u(x)|^ph(u(x))dx\leq C(n,p)\int_{\Omega} \left( \sqrt{ |\nabla^{(2)} u(x)||{\cal T}_{h,C}(u(x))|}\right)^{p}h(u(x))dx,$$ where $\Omega\subseteq {\bf R}^n$ and $n\ge 2$, $u:\Omega\rightarrow {\bf R}$ is in ... More

Hörmander's multiplier theorem for the Dunkl transformJul 07 2018For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. Denote by $dw(\mathbf x)=\prod_{\alpha\in R}|\langle \mathbf x,\alpha\rangle|^{k(\alpha)}\, d\mathbf x $ the associated ... More

Canonical tilting relative generatorsJan 30 2017Sep 18 2017Given a relatively projective birational morphism $f\colon X\to Y$ of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over $Y$) generators $T_{X,f}$ and $S_{X,f}$ in $\mathcal{D}^b(X)$. We develop a piece ... More

On semigroups generated by sums of even powers of Dunkl operatorsMay 17 2019On the Euclidean space $\mathbb R^N$ equipped with a normalized root system $R$, a multiplicity function $k\geq 0$, and the associated measure $dw(\mathbf x)=\prod_{\alpha\in R} |\langle \mathbf x,\alpha\rangle|^{k(\alpha)}d\mathbf x$ we consider the ... More

Independence characterization for Wishart and Kummer random matricesJun 29 2017May 15 2018We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let $X$ and $Y$ be independent, non-degenerate random variables valued in $(0, \infty)$, then $U= Y/(1+X)$ ... More

Fractional Variational Principle of HerglotzJun 03 2014The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought, by differential ... More

Generalized transversality conditions for the Hahn quantum variational calculusFeb 01 2012We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory.

Topological susceptibility from twisted mass fermions using spectral projectorsDec 12 2013We discuss the computation of the topological susceptibility using the method of spectral projectors and dynamical twisted mass fermions. We present our analysis concerning the O(a)-improvement of the topological susceptibility and we show numerical results ... More

The mass spectrum of the Schwinger model with Matrix Product StatesMay 16 2013Nov 10 2013We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new techniques to compute ... More

Characterizing the \lyaf\ flux probability distribution function using Legendre polynomialsAug 31 2016The Lyman-$\alpha$ forest is a highly non-linear field with a lot of information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper ... More

Ordering effects in 2D hexagonal systems of binary and ternary BCN alloysJun 17 2016We present theoretical study of ordering phenomena in binary $C_{1-x}B_{x}$ , $C_{1-x}N_{x}$ ternary $BC_{2}N$ alloys forming two-dimensional, graphene-like systems. For calculating energy of big systems (20 000 atoms in the supercell with periodic boundary ... More

On a variant of Hardy inequality between weighted Orlicz spacesMar 26 2009Let M be an N-function satisfying the $\Delta_2$- condition, let $\omega, \vp$ be two other functions, $\omega\ge 0$. We study Hardy-type inequalities \[ \int_{\rp} M(\omega (x)|u(x)|) {\rm exp}(-\vp (x))dx \le C\int_{\rp} M(|u'(x)|) {\rm exp}(-\vp (x))dx, ... More

Jack characters and enumeration of mapsNov 08 2016Jack characters provide dual information about Jack symmetric functions. We give explicit formulas for the top-degree part of these Jack characters in terms of bicolored oriented maps with an arbitrary face structure.

On a variant of Gagliardo-Nirenberg inequality deduced from HardyOct 30 2009We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.

Generalized Transversality Conditions in Fractional Calculus of VariationsJul 23 2012Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the Bolza-type fractional ... More

Computation of the chiral condensate using $N_f=2$ and $N_f=2+1+1$ dynamical flavors of twisted mass fermionsDec 12 2013We apply the spectral projector method, recently introduced by Giusti and L\"uscher, to compute the chiral condensate using $N_f=2$ and $N_f=2+1+1$ dynamical flavors of maximally twisted mass fermions. We present our results for several quark masses at ... More

Topological susceptibility and chiral condensate with $N_f=2+1+1$ dynamical flavors of maximally twisted mass fermionsNov 14 2011Mar 28 2012We study the 'spectral projector' method for the computation of the chiral condensate and the topological susceptibility, using $N_f=2+1+1$ dynamical flavors of maximally twisted mass Wilson fermions. In particular, we perform a study of the quark mass ... More

Bean Split Ratio for Dry Bean Canning Quality and Variety AnalysisMay 01 2019Splits on canned beans appear in the process of preparation and canning. Researchers are studying how they are influenced by cooking environment and genotype. However, there is no existing method to automatically quantify or to characterize the severity ... More

Bijection between oriented maps and weighted non-oriented mapsNov 07 2016We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map is counted ... More

Jacobi matrices on treesMar 20 2009Jul 09 2009Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always essentially ... More

Factorization property of generalized s-selfdecomposable measures and class $L^f$ distributions$^1$Dec 11 2008Dec 17 2008The method of \emph{random integral representation}, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we will find such ... More

The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivativeFeb 19 2010This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

A rational approximation method for the nonlinear eigenvalue problemJan 04 2019This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then to linearize the resulting ... More

Nonessential Functionals in Multiobjective Optimal Control ProblemsSep 26 2006We address the problem of obtaining well-defined criteria for multiobjective optimal control systems. Necessary and sufficient conditions for an optimal control functional to be nonessential are proved. The results provide effective tools for determining ... More

Non-invasive control of the fractional Hegselmann-Krause type modelAug 21 2017In this paper, the fractional order Hegselmann-Krause type model with leadership is studied.We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics. Necessary ... More

Competition of simple and complex adoption on multi-layer networksMay 11 2016Sep 15 2016We consider the competition of two mechanisms for adoption processes: a so-called complex threshold dynamics and a simple Susceptible-Infected-Susceptible (SIS) model. Separately, these mechanisms lead, respectively, to first order and continuous transitions ... More

The delta-nabla calculus of variationsDec 02 2009The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of ... More

The diamond-alpha Riemann integral and mean value theorems on time scalesApr 28 2008We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat's theorem for stationary points is also proved, as well as Rolle's, Lagrange's, and Cauchy's mean value theorems on time scales.

p-regularity theory. Applications and developmentsNov 12 2018We present recent advances in the analysis of constrained optimization problems with constraints given by singular mappings obtained within the framework of the $p$-regularity theory developed over the last twenty years. In particular, we address the ... More

A Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria OptimizationJun 08 2007The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function is called nonessential ... More

Towards a combined fractional mechanics and quantizationJun 05 2012A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional derivatives. ... More

Sequential weak continuity of null Lagrangians at the boundaryOct 04 2012We show weak* in measures on $\bar\O$/ weak-$L^1$ sequential continuity of $u\mapsto f(x,\nabla u):W^{1,p}(\O;\R^m)\to L^1(\O)$, where $f(x,\cdot)$ is a null Lagrangian for $x\in\O$, it is a null Lagrangian at the boundary for $x\in\partial\O$ and $|f(x,A)|\le ... More

Equilibrium states in dynamical systems via geometric measure theoryMar 28 2018Oct 25 2018Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds. We extend this ... More

Backward variational approach on time scales with an action depending on the free endpointsJan 04 2011We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales ... More

A General Backwards Calculus of Variations via DualityJul 09 2010We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for ... More

Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass ConditionMay 12 2009We introduce the notion of strong local minimizer for the problems of the calculus of variations on time scales. Simple examples show that on a time scale a weak minimum is not necessarily a strong minimum. A time scale form of the Weierstrass necessary ... More

A note on weak solutions of conservation laws and energy/entropy conservationJun 30 2017A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable ... More

The Hahn Quantum Variational CalculusJun 18 2010We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum ... More

Euler-Lagrange equations for composition functionals in calculus of variations on time scalesJul 04 2010In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta ... More

Natural Boundary Conditions in the Calculus of VariationsDec 03 2008We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.

A note on a composition of two random integral mappings $\J^\be$ and some examplesNov 23 2008A method of random integral representation, that is, a method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we show that a composition of ... More