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A new Cartan-type property and strict quasicoverings when $p=1$ in metric spacesJan 26 2018In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of $1$-finely open ... More

Critical ideals, minimum rank and zero forcing numberOct 10 2017There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical ideal is trivial. ... More

Some remarks on protolocalizations and protoadditive reflectionsFeb 28 2017Oct 29 2017We investigate additional properties of protolocalizations, introduced and studied by F. Borceux, M. M. Clementino, M. Gran, and L. Sousa, and of protoadditive reflections, introduced and studied by T. Everaert and M. Gran. Among other things we show ... More

Extremal behaviour in sectional matricesFeb 10 2017Oct 19 2017In this paper we want to revive the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprove recent results in this language. Moreover, some new results are shown ... More

On the regular conditional distribution of a multivariate Normal given a linear transformationDec 05 2016We show that the orthogonal projection operator onto the range of the adjoint of a linear operator T can be represented as UT, where U is an invertible linear operator. Using this representation we obtain a decomposition of a multivariate Normal random ... More

When the property of having a $π$-tree is preserved by productsNov 27 2016We find sufficient conditions under which the product of spaces that have a $\pi$-tree also has a $\pi$-tree. These conditions give new examples of spaces with a $\pi$-tree: every at most countable power of the Sorgenfrey line and every at most countable ... More

Species with potential arising from surfaces with orbifold points of order 2, Part II: arbitrary weightsNov 24 2016Let (\Sigma,M,O) be a surface with marked points and order-2 orbifold points which is either unpunctured or once-punctured closed, and let \omega be a function from O to {1,4}. For each triangulation \tau of (\Sigma,M,O) we construct a cochain complex ... More

Some results on the eventual paracanonical mapsNov 22 2016The eventual paracanonical map was introduced by Barja, Pardini, and Stoppino in order to prove refined Severi-type inequalities. We study the general structures of the eventual paracanonical maps by generic vanishing theory. In particular, we obtain ... More

Combinatorics of cyclic shifts in sylvester monoidsNov 13 2016The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. In the cyclic shift graph of the sylvester monoid (the monoid of binary search trees) of rank $n$, connected ... More

Identities in plactic, hypoplactic, sylvester, Baxter, and related monoidsNov 13 2016This paper considers whether non-trivial identities are satisfied by certain `plactic-like' monoids that, like the plactic monoid, are closely connected with combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic, and taiga ... More

Toughening by crack deflection in the homogenization of brittle composites with soft inclusionsNov 07 2016We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process. Because ... More

Sharp isoperimetric inequalities for small volumes in complete noncompact Riemannian manifolds of bounded geometry involving the scalar curvatureNov 05 2016We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with strong bounded geometry, as in Definition $2.3$, involving the scalar curvature function. Namely in strong bounded geometry, if the ... More

Sharp isoperimetric inequalities for small volumes in complete noncompact Riemannian manifolds of bounded geometry involving the scalar curvatureNov 05 2016Nov 11 2016We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with strong bounded geometry, as in Definition $2.3$, involving the scalar curvature function. Namely in strong bounded geometry, if the ... More

Plabic graphs and zonotopal tilingsNov 02 2016We say that two sets $S,T\subset\{1,2,\dots,n\}$ are chord separated if there does not exist a cyclically ordered quadruple $a,b,c,d$ of integers satisfying $a,c\in S-T$ and $b,d\in T-S$. This is a weaker version of Leclerc and Zelevinsky's weak separation. ... More

Two statements on path systems related to quantum minorsNov 01 2016In ArXiv:1604.00338[math.QA] we gave a complete combinatorial characterization of homogeneous quadratic identities for minors of quantum matrices. It was obtained as a consequence of results on minors of matrices of a special sort, the so-called path ... More

Classification of non-homogeneous Fourier matrices associated with modular data up to rank 5Oct 17 2016Modular data is an important topic of study in rational conformal field theory. A modular datum defines finite dimensional representations of the modular group $\mbox{SL}_2(\mathbf{Z})$. For every Fourier matrix in a modular datum there exists an Allen ... More

Classification of non-homogeneous Fourier matrices associated with modular data up to rank 5Oct 17 2016Nov 02 2016Modular data is an important topic of study in rational conformal field theory. A modular datum defines finite dimensional representations of the modular group $\mbox{SL}_2(\mathbf{Z})$. For every Fourier matrix in a modular datum there exists an Allen ... More

Classification of Homogeneous Fourier Matrices Associated with Modular DataOct 17 2016Modular data are commonly studied in mathematics and physics. A modular datum defines finite dimensional representations of the modular group $\mbox{SL}_2(\ZZ)$. For every Fourier matrix in a modular datum there exists a self-dual $C$-algebra. A Fourier ... More

Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Nov 30 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More

Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Dec 07 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More

Causal evolution of wave packetsOct 03 2016Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave packet formalism. We demonstrate that whereas the Dirac system is causal, the relativistic-Schr\"odinger ... More

Polish spaces of causal curvesSep 29 2016We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus obtained topological ... More

Inductive limits of finite dimensional hermitian symmetric spaces and K-theorySep 22 2016K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite dimensional hermitian ... More

Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularitySep 22 2016We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel measurable ... More

No positive cone in a free product is regularSep 20 2016We show that there exists no left order on the free product of two nontrivial, finitely generated, left-orderable groups such that the corresponding positive cone is represented by a regular language. Since there are orders on free groups of rank at least ... More

Dinv and AreaSep 15 2016We give a new combinatorial proof of the well known result that, when $m$ and $n$ are co-prime, the dinv of an $(m,n)$-Dyck path is equal to the area of its sweep map image. The first proof of this remarkable identity is due to Loehr and Warrington in ... More

The Inverse Gamma Distribution and Benford's LawSep 14 2016According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing in competitive ... More

On parking functions and the zeta map in types B,C and DSep 11 2016Let $\Phi$ be an irreducible crystallographic root system with Weyl group $W$, coroot lattice $\check{Q}$ and Coxeter number $h$. Recently the second named author defined a uniform $W$-isomorphism $\zeta$ between the finite torus $\check{Q}/(mh+1)\check{Q}$ ... More

Newton flows for elliptic functions II Structural stability: Classification & RepresentationSep 05 2016In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable and showed a ... More

Newton flows for elliptic functions I Structural stability: Characterization & GenericitySep 05 2016Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational ... More

The mechanical modes of a $2$-periodic triangulated surfaceSep 04 2016A recent "hidden symmetry" conjecture of B. Gin-ge Chen et al is resolved, concerning the dimension of the mechanical modes of a generic $2$-periodic triangulated surface $O$ in $R^3$ whose structure graph corresponds to a triangular tiling of $R^2$. ... More

Representation of convex geometries by circles on a planeSep 01 2016Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the result of K. Kashiwabara, ... More

Noncommutative reality-based algebras of rank 6Aug 30 2016We classify the RBA-bases of $6$-dimensional noncommutative semisimple algebras for which the algebra has a positive degree map. We show that these RBAs are parametrized by seven real numbers, the first four of which are positive and the remaining three ... More

Central elements in U(gl(n)), shifted symmetric functions and the superalgebraic Capelli's method of virtual variablesAug 24 2016Aug 30 2016In this work, we propose a new method for a unified study of some of the main features of the theory of the center of the enveloping algebra U(gl(n)) and of the algebra of shifted symmetric polynomials, that allows the whole theory to be developed, in ... More

Parabolic Kazhdan-Lusztig basis, Schubert classes, and equivariant oriented cohomologyAug 23 2016We study the equivariant oriented cohomology ring $h_T(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott-Samelson classes in $h_{T}(G/P)$ can ... More

Homological combinatorics and extensions of the cd-indexAug 22 2016Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to comprehensible ... More

Invariant Meromorphic Functions on the Wallpaper GroupsAug 19 2016We construct the meromorphic functions invariant under the action of the sense-preserving wallpaper groups on the complex plane. We discuss possible generalisa-tions of this to the general wallpaper groups. This provides the answer to a question posed ... More

Motzkin numbers and related sequences modulo powers of $2$Aug 19 2016We show that the generating function $\sum_{n\ge0}M_n\,z^n$ for Motzkin numbers $M_n$, when coefficients are reduced modulo a given power of $2$, can be expressed as a polynomial in the basic series $\sum _{e\ge0} ^{} {z^{4^e}}/( {1-z^{2\cdot 4^e}})$ ... More

Rules of Three for commutation relationsAug 17 2016Dec 04 2016We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of elements of a ring labeled by any subset of indices, it is enough that ... More

Rules of Three for commutation relationsAug 17 2016We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of elements of a ring labeled by any subset of indices, it is enough that ... More

The configuration space of a robotic arm in a tunnelAug 16 2016We study the motion of a robotic arm inside a rectangular tunnel. We prove that the configuration space of all possible positions of the robot is a CAT(0) cubical complex. This allows us to use techniques from geometric group theory to find the optimal ... More

Towards Boij-Söderberg theory for Grassmannians: the case of square matricesAug 14 2016We characterize the cone of GL-equivariant Betti tables of Cohen-Macaulay modules of codimension 1, up to rational multiple, over the coordinate ring of square matrices. This result serves as the base case for `Boij-S\"oderberg theory for Grassmannians', ... More

On the Surjectivity of Certain MapsAug 12 2016Nov 16 2016We prove in this article the surjectivity of three maps. We prove in Theorem $1$ the surjectivity of the chinese remainder reduction map associated to projective space of an ideal with a given factorization into ideals whose radicals are pairwise distinct ... More

Semigroups --- A Computational ApproachAug 10 2016Apr 06 2017The question whether there exists an integral solution to the system of linear equations with non-negative constraints, $A\x = \b, \, \x \ge 0$, where $A \in \Z^{m\times n}$ and ${\mathbf b} \in \Z^m$, finds its applications in many areas, such as operation ... More

Semigroups --- A Computational ApproachAug 10 2016The question whether there exists an integral solution to the system of linear equations with non-negative constraints, $A\x = \b, \, \x \ge 0$, where $A \in \Z^{m\times n}$ and ${\mathbf b} \in \Z^m$, finds its applications in many areas, such as operation ... More

Syzygies of bounded rank symmetric tensors are generated in bounded degreeAug 05 2016We study the syzygies of secant ideals of Veronese subrings of a fixed commutative graded algebra over a field of characteristic 0. One corollary is that the degrees of the minimal generators of the ith syzygy module of the coordinate ring of the rth ... More

Strong failures of higher analogs of Hindman's theoremAug 04 2016Nov 22 2016We show that various analogs of Hindman's Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1: There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that for every $X\subseteq\mathbb R$ with ... More

Strong failures of higher analogs of Hindman's theoremAug 04 2016Sep 24 2016We show that various analogs of Hindman's Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1: There is a proper class of uncountable cardinals $\kappa$ satisfying the following statement: For every commutative ... More

Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order DynamicsAug 04 2016Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry principles and the ... More

A spectral theory for simply periodic solutions of the sinh-Gordon equationJul 29 2016In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral data is described ... More

On the roots of the node reliability polynomialJul 28 2016Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational nodes can all communicate ... More

Classifying Poincaré Inequalities and the local geometry of RNP-Differentiability SpacesJul 25 2016We give a classification of doubling metric measure spaces admitting a $(1,p)$-Poincar\'e inequality for some $p$ in terms of connectivity and without reference to modulus estimates. Further we give a classification of spaces that are rectifiable with ... More

Classifying Poincaré Inequalities and the local geometry of RNP-Differentiability SpacesJul 25 2016Nov 02 2016We give a new condition on a metric measure space guaranteeing a $(1,p)$-Poincar\'e inequality for some $p$. This condition doesn't use a modulus of a curve family, is technically more flexible and allows for several applications. We also introduce an ... More

Generalized Bogomolov-Gieseker type inequalities on Fano 3-foldsJul 25 2016Jul 28 2016We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projective 3-folds. We give an equivalent conjecture which needs to check these ... More

Preopen sets in bispacesJul 24 2016The notion of preopen sets and precontinuity in a topological space was introduced by Mashhour et. al in 1982 [13]. Later the same was studied in a bitopological space in [7] and [9]. Here we have studied the idea of pairwise preopen sets (semi preopen) ... More

Inference for Multivariate Regression Model based on synthetic data generated under Fixed-Posterior Predictive Sampling: comparison with Plug-in SamplingJul 21 2016The authors derive likelihood-based exact inference methods for the multivariate regression model, for singly imputed synthetic data generated via Posterior Predictive Sampling (PPS) and for multiply imputed synthetic data generated via a newly proposed ... More

The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homologyJul 21 2016The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that ... More

Exterior power operations on higher $K$-groups via binary complexesJul 06 2016Oct 18 2016We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a $\lambda$-ring, ... More

Exterior power operations on higher $K$-groups via binary complexesJul 06 2016Jul 20 2016We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a $\lambda$-ring, ... More

Canonical idempotents of multiplicity-free families of algebrasJun 28 2016Any multiplicity-free family of finite dimensional algebras has a canonical complete set of of pairwise orthogonal primitive idempotents in each level. We give various methods to compute these idempotents. In the case of symmetric group algebras over ... More

Min-max formulas for nonlocal elliptic operatorsJun 27 2016In this work, we give a characterization of Lipschitz operators on spaces of $C^2(M)$ functions (also $C^{1,1}$, $C^{1,\gamma}$, $C^1$, $C^\gamma$) that obey the global comparison property-- i.e. those that preserve the global ordering of input functions ... More

Min-max formulas for nonlocal elliptic operatorsJun 27 2016Oct 25 2016In this work, we give a characterization of Lipschitz operators on spaces of $C^2(M)$ functions (also $C^{1,1}$, $C^{1,\gamma}$, $C^1$, $C^\gamma$) that obey the global comparison property-- i.e. those that preserve the global ordering of input functions ... More

Epsilon-strongly graded rings, separability and semisimplicityJun 24 2016Aug 25 2016We introduce the class of epsilon-strongly graded rings and show that it properly contains both the collection of strongly graded rings and the family of unital partial crossed products. We determine when epsilon-strongly graded rings are separable over ... More

The area integral and boundary values of octonion-valued monogenic functionsJun 22 2016We introduce the Area Integral for octonion-valued monogenic functions in the half-space. It is used to prove the ex- istence of the non-tangential boundary values almost everywhere and of the normal boundary values at a given boundary point for these ... More

Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometryJun 16 2016For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is a locally $\left(1-\frac{1}{n}\right)$-H\"older continuous function and so in particular it is continuous. ... More

Quivers with subadditive labelings: classification and integrabilityJun 15 2016Strictly subadditive, subadditive and weakly subadditive labelings of quivers were introduced by the second author, generalizing Vinberg's definition for undirected graphs. In our previous work we have shown that quivers with strictly subadditive labelings ... More

Moments and Entropy of the Interpolating Family of Size DistributionsJun 15 2016Sinner et al. (2016) recently introduced a five-parameter family of size distributions, coined Interpolating Family or IF distribution for short. In this complementary note, we take advantage of the tractability of the IF distribution to compute the moments ... More

A new characterisation of groups amongst monoidsJun 08 2016We prove that a monoid $M$ is a group if and only if, in the category of monoids, all points over $M$ are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo and Van der Linden which characterises groups amongst monoids as the protomodular ... More

Frankl's Conjecture for subgroup latticesMay 31 2016Jun 21 2016We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common technical result ... More

The further chameleon groups of Richard Thompson and Graham Higman: Automorphisms via dynamics for the Higman groups $G_{n,r}$May 30 2016We characterise the automorphism groups of the Higman groups $G_{n,r}$ as groups of specific homeomorphisms of Cantor spaces $\mathfrak{C}_{n,r}$, through the use of Rubin's theorem. This continues a thread of research begun by Brin, and extended later ... More

Solution to HJB equations with an elliptic integro-differential operator and gradient constraintMay 17 2016Nov 29 2016The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton-Jacobi-Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises ... More

Solution to HJB equations with an elliptic integro-differential operator and gradient constraintMay 17 2016Oct 07 2016The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton-Jacobi-Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises ... More

The bellows conjecture for small flexible polyhedra in non-Euclidean spacesMay 15 2016The bellows conjecture claims that the volume of any flexible polyhedron of dimension 3 or higher is constant during the flexion. The bellows conjecture was proved for flexible polyhedra in the Euclidean spaces of dimensions 3 and higher, and for bounded ... More

Every filter is homeomorphic to its squareMay 13 2016We show that every filter $\mathcal{F}$ on $\omega$, viewed as a subspace of $2^\omega$, is homeomorphic to $\mathcal{F}^2$. This generalizes a theorem of van Engelen, who proved that this holds for Borel filters.

A topological version of Hilbert's NullstellensatzMay 10 2016We prove that the space of radical ideals of a ring $R$, endowed with the hull-kernel topology, is a spectral space, and that it is canonically homeomorphic to the space of the nonempty Zariski closed subspaces of Spec$(R)$, endowed with a Zariski-like ... More

Nakayama Automorphism and Rigidity of Dual Reflections Group CoactionsMay 06 2016We study homological properties and rigidity of group coactions on Artin-Schelter regular algebras.

Combinatorial Aspects of the Distribution of Rough ObjectsMay 05 2016The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent's view about crisp and non crisp objects over a set of objects has a rough ... More

Dualité et principe local-global sur des corps locaux de dimension 2May 04 2016Let $k$ be an algebraically closed field, a finite field or a $p$-adic field. Let $K_0=k((x,y))$ be the field of Laurent series in two variables over $k$. We define Tate-Shafarevich groups of a commutative group scheme over $K_0$ via cohomology classes ... More

Dynamics of Discrete Time Systems with a Hysteresis Stop OperatorMay 02 2016May 03 2016We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are studied depending on two parameters. The system is motivated by modifications ... More

The Dirichlet problem for p-harmonic functions with respect to arbitrary compactificationsApr 29 2016We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron solutions. We ... More

Third order variational equation for the free relativistic topApr 24 2016I proffer a development of some third order equation of motion for the free relativistic top from the simultaneously imposed assumptions of variationality and Lorentz symmetry.

Carleson measures for Hilbert spaces of analytic functions on the complex half-planeApr 20 2016Aug 06 2016The notion of a Carleson measure was introduced by Lennart Carleson in his proof of the Corona Theorem for $H^\infty(\mathbb{D})$. In this paper we will define it for certain type of reproducing kernel Hilbert spaces of analytic functions of the complex ... More

Horizontal $α$-Harmonic MapsApr 19 2016Given a $C^1$ planes distribution $P_T$ on all ${\mathbb R}^m$ we consider {\em horizontal $\alpha$-harmonic maps}, $\alpha\ge 1/2$, with respect to such a distribution. These are maps $u\in H^{\alpha}({{\mathbb R}}^k,{{\mathbb R}}^m)$ satisfying $P_T\nabla ... More

Differential geometric mechanisms in Ostrohrads'kyj relativistic spherical top dynamicsApr 16 2016Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The main goal is ... More

Bialgebra and Hopf algebra structures on free Rota-Baxter algebrasApr 12 2016In this paper, we obtain a canonical factorization of basis elements in free Rota-Baxter algebras built on bracketed words. This canonical factorization is applied to give a coalgebra structure on the free Rota-Baxter algebras. Together with the Rota-Baxter ... More

A broad class of shellable latticesApr 11 2016We introduce a new class of lattices, the modernistic lattices, and their duals, the comodernistic lattices. We show that every modernistic or comodernistic lattice has shellable order complex. We go on to exhibit a large number of examples of (co)modernistic ... More

Arithmetical structures of graphsApr 08 2016Jun 21 2016The arithmetical structures of a graph was introduced by Lorenzini in~\cite{Lorenzini89} as some intersection matrices that arise in the study of degenerating curves in algebraic geometry. We study arithmetical structures of the complete graph, the path ... More

Cauchy-Davenport type inequalities, IApr 07 2016May 04 2016Let $\mathbb G = (G, +)$ be a group (either abelian or not). Given $X, Y \subseteq G$, we denote by $\langle Y \rangle$ the subsemigroup of $\mathbb G$ generated by $Y$, and we set $$\gamma(Y) := \sup_{y_0 \in Y} \inf_{y_0 \ne y \in Y} {\rm ord}(y - y_0)$$ ... More

On Quillen's conjecture for p-solvable groupsApr 07 2016We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without employing it.

On n-Trivial Extensions of RingsApr 06 2016Oct 01 2016The notion of trivial extension of a ring by a module has been extensively studied and used in ring theory as well as in various other areas of research like cohomology theory, representation theory, category theory and homological algebra. In this paper ... More

Path systems in certain planar graphs and quadratic identities for quantum minorsApr 01 2016We deal with weighted planar graphs $G$, called \emph{grid-shaped} ones, arising as a natural generalization of the graphs associated to Cauchon diagrams. Adapting an approach due to Casteels, we consider a matrix $Path_G$ generated by paths in $G$, whose ... More

Poset edge densities, nearly reduced words, and barely set-valued tableauxMar 31 2016May 10 2016In certain finite posets, the expected down-degree of their elements is the same whether computed with respect to either the uniform distribution or the distribution weighting an element by the number of maximal chains passing through it. We show that ... More

Pasting and Reversing Approach to Matrix TheoryMar 23 2016Aug 16 2016The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing. We start giving a summary of previous results concerning to Pasting and Reversing over vectors and matrices, after we rewrite such properties of Pasting and ... More

Parametric representation of univalent functions with boundary regular fixed pointsMar 13 2016Mar 30 2016Given a set $\mathfrak S$ of conformal maps of the unit disk $\mathbb D$ into itself that is closed under composition, we address the question whether $\mathfrak S$ can be represented as the reachable set of a Loewner - Kufarev - type ODE $\mathrm{d}w_t/\mathrm{d}t=G_t\circ ... More

The classification of Zamolodchikov periodic quiversMar 12 2016Apr 01 2016Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity ... More

Six Functor Formalisms and Fibered MultiderivatorsMar 07 2016We define abstract six-functor-formalisms using the theory of (op)fibrations of 2-multicategories. We also give axioms for a Wirthm\"uller and Grothendieck formalism (where either $f_!=f_*$ or $f^!=f^*$) or intermediate formalisms (where we have e.g. ... More

Pluriassociative algebras II: The polydendriform operad and related operadsMar 04 2016Dendriform algebras form a category of algebras recently introduced by Loday. A dendriform algebra is a vector space endowed with two nonassociative binary operations satisfying some relations. Any dendriform algebra is an algebra over the dendriform ... More

Pluriassociative algebras I: The pluriassociative operadMar 03 2016Mar 04 2016Diassociative algebras form a categoy of algebras recently introduced by Loday. A diassociative algebra is a vector space endowed with two associative binary operations satisfying some very natural relations. Any diassociative algebra is an algebra over ... More

3-nets realizing a diassociative loop in a projective planeMar 01 2016A \textit{$3$-net} of order $n$ is a finite incidence structure consisting of points and three pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with exactly one line ... More

Free subgroup numbers modulo prime powers: the non-periodic caseFeb 28 2016In [J. Algebra 452 (2016), 372-389], we characterise when the sequence of free subgroup numbers of a finitely generated virtually free group $\Gamma$ is ultimately periodic modulo a given prime power. Here, we show that, in the remaining cases, in which ... More