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Many mathematicians have studied the algebraic independence over Q of the values of gap series, and the values of lacunary series satisfying functional equations of Mahler type. In this paper, we give a new criterion for the algebraic independence over Q of the values ∑∞n=0t(n)β−n for distinct sequences (t(n))∞n=0 of nonnegative integers, where β is a fixed Pisot or Salem number. Our criterion is applicable to certain power series which are not lacunary. Moreover, our criterion does not use functional equations. Consequently, we deduce the algebraic independence of certain values ∑∞n=0t1(n)β−n,…,∑∞n=0tr(n)β−n satisfying

Universal extensions arise naturally in the Auslander bijections. For an abelian category having Auslander–Reiten duality, we exploit a bijection triangle, which involves the Auslander bijections, universal extensions and the Auslander–Reiten duality. Some consequences are given, in particular, a conjecture by Ringel is verified.

This article is a direct continuation of [B]. It contains a simple proof of comparison theorems in p-adic Hodge theory (the Fontaine-Jannsen conjecture). Different proofs were found earlier by Faltings, Niziol, and Tsuji, the case of open varieties treated by Yamashita. An alternative approach, based on an identification of the log crystalline cohomology for lci maps with the noncompleted (for the Hodge filtration) derived de Rham complex, was developed by Bhatt [Bh2].

In preparation for gray zone or conventional warfare conducted by Russian or Chinese adversaries and their proxies, threatened nations can apply a Total Defense approach to safeguard their territorial integrity and political sovereignty. Two key components for any effective Total Defense concept are national special operations forces (SOF) and volunteer, citizen-soldier territorial defense forces (TDF). This article examines the role of special operations forces as significant multi-dimensional, entrepreneurial integrators in Total Defense. In particular, it demonstrates the symbiotic relationship between special operations and territorial defense forces in the complex mission of national resistance during crisis and occupation.

Straipsnyje analizuojamas paskutinis lietuvių rašytojo Ričardo Gavelio romanas „Sun-Tzu gyvenimas šventame Vilniaus mieste“. Pagrindinis dėmesys skiriamas kūri nio protagonisto savimonei ir santykiui su Vilniaus miesto tikrove nagrinėti. Straipsnyje taip pat aptariami ankstesnieji tekstai, kuriuose kalbama apie minėtą Gavelio romaną: Violetos Kelertienės pokolonijinių tyrimų ir Jūratės Čerškutės disertacinio dekonstrukcinio darbo išva dos. Straipsnio pabaigoje išvedama, kad pagrindinis „Sun-Tzu gyvenimo šventame Vilniaus mieste“ veikėjas yra specifiškai susijęs su pačiu autoriumi ir jo lūpomis perteikiamas galutinis, testamentinis Gavelio pasaulėvaizdis ir atsakymai į viso gyvenimo klausimus: kas nulemia neapykantą Vilniui ir koks yra individo vaidmuo istoriniame kontekste, prie kurio pritapti nie kada nesiekta ir net nebandyta? Žmogiškoji būtis Gaveliui – tai permanentinis karas su tikrais ar įsivaizduojamais priešais. Paskutiniame romane ši kova vyksta daugiausia požeminiame, pogrin džio Vilniuje – alternatyvioje autoriaus tikrovėje.

In this paper, we study the stochastic three-dimensional modified Leray-alpha model arising from the turbulent flows of fluids. We prove the existence of the probabilistic weak solution under the non-Lipschitz condition for the nonlinear forcing terms. We also discuss its uniqueness.

In this paper, we study the stochastic three-dimensional modified Leray-alpha model arising from the turbulent flows of fluids. We prove the existence of the probabilistic weak solution under the non-Lipschitz condition for the nonlinear forcing terms. We also discuss its uniqueness.

The paper discusses several techniques which may be used for applying the coupling method to solutions of stochastic differential equations (SDEs). The coupling techniques traditionally consist of two components: one is local mixing, the other is recurrence. Often in the articles they do not split. Yet, they are quite different in their nature, and this paper separates them, concentrating only on the former.

The paper discusses several techniques which may be used for applying the coupling method to solutions of stochastic differential equations (SDEs). The coupling techniques traditionally consist of two components: one is local mixing, the other is recurrence. Often in the articles they do not split. Yet, they are quite different in their nature, and this paper separates them, concentrating only on the former.