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1742. A note on model structures on arbitrary Frobenius categories
- Creator:
- Li, Zhi-Wei
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, Frobenius categorie, triangulated categories, model structure, 13, and 51
- Language:
- English
- Description:
- We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category F such that the homotopy category of this model structure is equivalent to the stable category F as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When F is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed) model structure in the sense of Gillespie (2011)., Zhi-Wei Li., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1743. A note on normal varieties of monounary algebras
- Creator:
- Chajda, Ivan and Länger, Helmut
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- monounary algebra, variety, normal variety, and choice algebra
- Language:
- English
- Description:
- A variety is called normal if no laws of the form $s=t$ are valid in it where $s$ is a variable and $t$ is not a variable. Let $L$ denote the lattice of all varieties of monounary algebras $(A,f)$ and let $V$ be a non-trivial non-normal element of $L$. Then $V$ is of the form ${\mathrm Mod}(f^n(x)=x)$ with some $n>0$. It is shown that the smallest normal variety containing $V$ is contained in ${\mathrm HSC}({\mathrm Mod}(f^{mn}(x)=x))$ for every $m>1$ where ${\mathrm C}$ denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of $L$ consisting of all normal elements of $L$ is isomorphic to $L$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1744. A note on on-line ranking number of graphs
- Creator:
- Semanišin, Gabriel and Soták, Roman
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- on-line ranking number, complete $n$-partite graph, and hereditary and additive properties of graphs
- Language:
- English
- Description:
- A $k$-ranking of a graph $G=(V,E)$ is a mapping $\varphi \:V \rightarrow \lbrace 1,2,\dots ,k\rbrace $ such that each path with endvertices of the same colour $c$ contains an internal vertex with colour greater than $c$. The ranking number of a graph $G$ is the smallest positive integer $k$ admitting a $k$-ranking of $G$. In the on-line version of the problem, the vertices $v_1,v_2,\dots ,v_n$ of $G$ arrive one by one in an arbitrary order, and only the edges of the induced graph $G[\lbrace v_1,v_2,\dots ,v_i\rbrace ]$ are known when the colour for the vertex $v_i$ has to be chosen. The on-line ranking number of a graph $G$ is the smallest positive integer $k$ such that there exists an algorithm that produces a $k$-ranking of $G$ for an arbitrary input sequence of its vertices. We show that there are graphs with arbitrarily large difference and arbitrarily large ratio between the ranking number and the on-line ranking number. We also determine the on-line ranking number of complete $n$-partite graphs. The question of additivity and heredity is discussed as well.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1745. A note on one-dimensional stochastic equations
- Creator:
- Engelbert, Hans-Jürgen
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- one-dimensional stochastic equations, time-dependent diffusion coefficients, Brownian motion, existence of solutions, uniqueness in law, continuous local martingales, and representation property
- Language:
- English
- Description:
- We consider the stochastic equation \[ X_t=x_0+\int _0^t b(u,X_{u})\mathrm{d}B_u,\quad t\ge 0, \] where $B$ is a one-dimensional Brownian motion, $x_0\in \mathbb{R}$ is the initial value, and $b\:[0,\infty )\times \mathbb{R}\rightarrow \mathbb{R}$ is a time-dependent diffusion coefficient. While the existence of solutions is well-studied for only measurable diffusion coefficients $b$, beyond the homogeneous case there is no general result on the uniqueness in law of the solution. The purpose of the present note is to give conditions on $b$ ensuring the existence as well as the uniqueness in law of the solution.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1746. A note on plural logic
- Creator:
- Fernandéz Díez, Gustavo
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- compound terms, itemized predication, singular logic, and plural logic
- Language:
- Slovak
- Description:
- A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And as a result, inferences such as ''Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle'' are shown to be first-order., Rozlišování se zavádí mezi rozčleněným množstvím a nerozdělením množných predikcí. Tvrdí se, že plnohodnotný systém pluralitní logiky není nutný pro to, aby bylo možné zohlednit platnost závěrů týkajících se skupinového predikce. Místo toho je ukázáno, jak lze tento typ závěrů adekvátně řešit v logickém systému prvního řádu, po malých úpravách standardního zpracování. Navrhovaný systém, na rozdíl od množné logiky, má výhodu zachování úplnosti. Výsledkem je, že závěry jako ,,Dick a Tony vyprázdnili láhev, proto Tony a Dick vyprázdnili láhev''., and Gustavo Fernandéz Díez
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1747. A note on predicition for discrete time series
- Creator:
- Morvai, Gusztáv and Weiss, Benjamin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- nonparametric estimation and stationary processes
- Language:
- English
- Description:
- Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X and that f(X) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λn along which we will be able to estimate the conditional expectation E(f(Xλn+1)|X0,…,Xλn) from the observations (X0,…,Xλn) in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series which includes among others all stationary and ergodic finitarily Markovian processes. If the stationary and ergodic process turns out to be finitarily Markovian (in particular, all stationary and ergodic Markov chains are included in this class) then limn→∞nλn>0 almost surely. If the stationary and ergodic process turns out to possess finite entropy rate then λn is upper bounded by a polynomial, eventually almost surely.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1748. A note on principal ideals and $\Cal J$-classes in the direct product of two semigroups
- Creator:
- Fabrici, Imrich
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- math, semigroups, and principal ideals
- Language:
- English
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1749. A note on radio antipodal colourings of paths
- Creator:
- Khennoufa, Riadh and Togni, Olivier
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- radio antipodal colouring, radio number, and distance labeling
- Language:
- English
- Description:
- The radio antipodal number of a graph G is the smallest integer c such that there exists an assignment f : V (G) → {1, 2, . . . , c} satisfying |f(u) − f(v)| ≥ D − d(u, v) for every two distinct vertices u and v of G, where D is the diameter of G. In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57– 69]. We also show the connections between this colouring and radio labelings.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1750. A note on representing dowling geometries by partitions
- Creator:
- Matúš, František and Ben-Efraim, Aner
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- kybernetika, cybernetics, matroid representations, partition representations, Dowling geometries, Frobenius groups, 23, and 007
- Language:
- English
- Description:
- We prove that a rank ≥3 Dowling geometry of a group H is partition representable if and only if H is a Frobenius complement. This implies that Dowling group geometries are secret-sharing if and only if they are multilinearly representable., František Matúš and Aner Ben-Efraim., and Obsahuje bibliografické odkazy
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public