A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences determining the 2-acyclicity of the symbol of the corresponding differential operator. Therefore the system is not integrable and higher order obstruction exists., Tamás Milkovszki, Zoltán Muzsnay., and Seznam literatury
Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality $\|p'\|_{[-1,1]}\leq\frac12\|p\|_{[-1,1]}$ for a constrained polynomial $p$ of degree at most $n$, initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval $(-1,1)$ and establish a new asymptotically sharp inequality., Lai-Yi Zhu, Da-Peng Zhou., and Obsahuje bibliografii
We examine the q-Pell sequences and their applications to weighted partition theorems and values of L-functions. We also put them into perspective with sums of tails. It is shown that there is a deeper structure between two-variable generalizations of Rogers-Ramanujan identities and sums of tails, by offering examples of an operator equation considered in a paper published by the present author. The paper starts with the classical example offered by Ramanujan and studied by previous authors noted in the introduction. Showing that simple combinatorial manipulations give rise to an identity published by the present author, a weighted form of a Lebesgue partition theorem is given as the main application to partitions. The conclusion of the paper summarizes some directions for further research, pointing out that certain conditions on the q-polynomial would be desired, and also possibly looking at the operator equation in the present paper from the position of using modular forms., Alexander E. Patkowski., and Obsahuje bibliografii
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are introduced: quantum group of gauge transformations, Pontryagin dual of a quantum group, and Galois-Hopf-algebra of an algebra extension., Maysam Maysami Sadr., and Obsahuje bibliografii
In this paper we study the regularity properties of the one-dimensional one-sided Hardy-Littlewood maximal operators M+ and M−. More precisely, we prove that M+ and M− map W¹,p(R) → W1,p(R) with 1 < p < nekonečno, boundedly and continuously. In addition, we show that the discrete versions M+ and M− map BV(ℤ) → BV(ℤ) boundedly and map l¹(ℤ) → BV(ℤ) continuously. Specially, we obtain the sharp variation inequalities of M+ and M−, that is Var(M+(f))<Var(f) and Var(M−(f))<Var(f) if f ∈ BV(ℤ), where Var(f) is the total variation of f on ℤ and BV(ℤ) is the set of all functions f: ℤ → R satisfying Var(f) < nekonečno., Feng Liu, Suzhen Mao., and Obsahuje bibliografii
At the end of 2010 seven TM 71 extensometers, installed at or near the active faults in Slovenia, were in operation. Three of them are on the surface and four inside karst caves. The highest rates with stable sense of movements were observed on the Idrija fault. Average horizontal displacement rate was 0.24 mm/year. Short term rates were even greater and reached 0.54 mm/year. The Raša fault first experienced an uplift of the SW block of 0.16 mm/year, which was followed by a short-term down-slip of the same block at the rate of 0.37 mm/year. Later the sense of movement returned to uplift with a rate of 0.05 mm/year. The average horizontal displacement was 0.07 mm/year. The Kneža fault experienced very small average displacements (y=0.035 mm/year, z=0.03 mm/year and x=0.02 mm/year). Similar rates were observed in nearby Polog cave (y=0.015 mm/year, z=0.027 mm/year and x=0.016 mm/year), which is located close to the seismically active Ravne fault. For Kostanjevica cave, located near the Brežice fault, small average rates are characteristic (y=0.006 mm/year, z=0.017 mm/year and x=0.012 mm/year). In Postojna cave, located close to the Predjama fault, two monitoring sites are very stable with small tectonic movements, including general dextral horizontal movement of 0.05 mm from 2004 to 2010 (Postojna 1) and two significant short-term peaks of 0.08 mm (Postojna 1-y and Postojna 2-z)., Andrej Gosar, Stanka Šebela, Blahoslav Košťák and Josef Stemberk., and Obsahuje bibliografii
Let K be a field and S = K[x1, ..., xm, y1,..., yn] be the standard bigraded polynomial ring over K. In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” S-modules with respect to Q = (y1, ..., yn). Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to Q in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to Q are considered., Leila Parsaei Majd, Ahad Rahimi., and Obsahuje seznam literatury
For any two positive integers n and k\geqslant 2, let G(n, k) be a digraph whose set of vertices is {0, 1, ..., n − 1} and such that there is a directed edge from a vertex a to a vertex b if ak ≡ b (mod n). Let n = \prod\nolimits_{i = 1}^r {p_i^{{e_i}}} be the prime factorization of n. Let P be the set of all primes dividing n and let P_{1},P_{2} \subseteq P be such that P_{1\cup P_{2}}= P and P_{1\cup P_{2}}=\emptyset . A fundamental constituent of G(n, k), denoted by G_{{P_2}}^*(n,k), is a subdigraph of G(n, k) induced on the set of vertices which are multiples of \prod\nolimits_{{p_i} \in {P_2}} {{p_i}} and are relatively prime to all primes q\in P_{1}. L. Somer and M. Křižek proved that the trees attached to all cycle vertices in the same fundamental constituent of G(n, k) are isomorphic. In this paper, we characterize all digraphs G(n, k) such that the trees attached to all cycle vertices in different fundamental constituents of G(n, k) are isomorphic. We also provide a necessary and sufficient condition on G(n, k) such that the trees attached to all cycle vertices in G(n, k) are isomorphic., Amplify Sawkmie, Madan Mohan Singh., and Obsahuje seznam literatury
Oncocytic Schneiderian papilloma (OSP) is one of the three morphologically distinct tumors that arise from Schneiderian membrane (the others include exophytic papilloma and inverted papilloma). OSP almost always occurs unilaterally in the paranasal sinuses, usually in the maxillary sinus, ethmoid cells or sphenoid sinus. We report a case of a 64-year-old woman with OSP arising from the left frontal sinus. In the report herein, we describe an OSP originating in the region of frontal sinus, which, to the best of our knowledge, represents the first documented example in English literature of OSP developing in this anatomical site. and D. Kalfert, J. Laco, P. Celakovský, K. Smatanová, M. Ludvíková
Ongoing interest in brain ischemia research has provided data showing that ischemia may be involved in the pathogenesis of Alzheimer disease. Brain ischemia in the rat produces a stereotyped pattern of selectiv e neuronal degeneration, which mimics early Alzheimer disease pathology. The objective of this study was to further develop an d characterize cardiac arrest model in rats, which provides practical way to analyze Alzheimer- type neurodegeneration. Rats were made ischemic by cardiac arrest. Blood-brain barrier (BBB) insufficiency, accumulation of different parts of amyloid precursor protein (APP) and platelets inside and outside BBB vessels were investigated in ischemic brain up to 1-year survival. Isch emic brain tissue demonstrated haphazard BBB changes. Toxic fr agments of APP deposits were associated with the BBB vessels. Moreover our study revealed platelet aggregates in- and outside BBB vessels. Toxic parts of APP and platelet aggregates correlated very well with BBB permeability. Progressive injury of the ischemic brain parenchyma may be caused not only by a degeneration of neurons destroyed during ischemia but also by chronic damage in BBB. Chronic ischemic BBB insufficiency with accumulation of toxic components of APP in the brain tissue perivascular space, may gradually over a lifetime, progress to brain atrophy and to full blown Alzheimer-type pathology., M. Jabłoński., and Obsahuje bibliografii a bibliografické odkazy