Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Fundamental Investigations on the Isomorphism of Commutative Group Algebras in Bulgaria

The isomorphism problem of arbitrary algebraic structures plays always a central role in the study of a given algebraic object. In this paper we give the first investigations and also some basic results on the isomorphism problem of commutative group algebras in Bulgaria.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

Involution Matrix Algebras – Identities and Growth

2000 Mathematics Subject Classification: 16R50, 16R10.

Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

2000 Mathematics Subject Classification: 16R10, 16R30.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

On Local Uniform Topological Algebras

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.

Semi-Symmetric Algebras: General Constructions. Part II

2000 Mathematics Subject Classification: 15A69, 15A78.

Free Bicommutative Algebras

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.

Growth of some varieties of Leibniz-Poisson algebras

2010 Mathematics Subject Classification: 17A32, 17B63.

Lie-szimmetriák egy közgazdasági alkalmazása (An economic application of the Lie symmetries)

Ebben a tanulmányban ismertetjük a Nöther-tétel lényegi vonatkozásait, és kitérünk a Lie-szimmetriák értelmezésére abból a célból, hogy közgazdasági folyamatokra is alkalmazzuk a Lagrange-formalizmuson nyugvó elméletet. A Lie-szimmetriák dinamikai rendszerekre történő feltárása és viselkedésük jellemzése a legújabb kutatások eredményei e területen. Például Sen és Tabor (1990), Edward Lorenz (1963), a komplex kaotikus dinamika vizsgálatában jelent®s szerepet betöltő 3D modelljét, Baumann és Freyberger (1992) a két-dimenziós Lotka-Volterra dinamikai rendszert, és végül Almeida és Moreira (1992) a három-hullám interakciós problémáját vizsgálták a megfelelő Lie-szimmetriák segítségével. Mi most empirikus elemzésre egy közgazdasági dinamikai rendszert választottunk, nevezetesen Goodwin (1967) ciklusmodelljét. Ennek vizsgálatát tűztük ki célul a leírandó rendszer Lie-szimmetriáinak meghatározásán keresztül. / === / The dynamic behavior of a physical system can be frequently described very concisely by the least action principle. In the centre of its mathematical presentation is a specic function of coordinates and velocities, i.e., the Lagrangian. If the integral of the Lagrangian is stationary, then the system is moving along an extremal path through the phase space, and vice versa. It can be seen, that each Lie symmetry of a Lagrangian in general corresponds to a conserved quantity, and the conservation principle is explained by a variational symmetry related to a dynamic or geometrical symmetry. Briey, that is the meaning of Noether's theorem. This paper scrutinizes the substantial characteristics of Noether's theorem, interprets the Lie symmetries by PDE system and calculates the generators (symmetry vectors) on R. H. Goodwin's cyclical economic growth model. At first it will be shown that the Goodwin model also has a Lagrangian structure, therefore Noether's theorem can also be applied here. Then it is proved that the cyclical moving in his model derives from its Lie symmetries, i.e., its dynamic symmetry. All these proofs are based on the investigations of the less complicated Lotka Volterra model and those are extended to Goodwin model, since both models are one-to-one maps of each other. The main achievement of this paper is the following: Noether's theorem is also playing a crucial role in the mechanics of Goodwin model. It also means, that its cyclical moving is optimal. Generalizing this result, we can assert, that all dynamic systems' solutions described by first order nonlinear ODE system are optimal by the least action principle, if they have a Lagrangian.

Paleoenvironments and geochemical signals from the late Barremian to the middle Aptian in a Tethyan marginal basin, northeast Spain: Implications for carbon sequestration in restricted basins

The hallmark of oceanic anoxic event 1a (OAE1a) (early Aptian ~125 Ma) corresponds to worldwide deposition of black shales with total organic carbon (TOC) content > 2% and a δ13C positive excursion up to ~5‰. OAE1a has been related to large igneous province volcanism and dissociation of methane hydrates during the Lower Cretaceous. However, the occurrence of atypical, coeval and diachronous organic-rich deposits associated with OAE1a, which are also characterized by positive spikes of the δ 13C in epicontinental to restricted marine environments of the Tethys Ocean, indicates localized responses decoupled from complex global forcing factors. ^ The present research is a high-resolution, multiproxy approach to assess the paleoenvironmental conditions that led to enhanced carbon sequestration from the late Barremian to the middle Aptian in a restricted, Tethyan marginal basin prior to and during OAE1a. I studied the lower 240 m of the El Pui section, Organyà Basin, Spanish Pyrenees. The basin developed as the result of extensional tectonism linked to the opening of the Atlantic Ocean. At the field scale the section consists of a sequence of alternating beds of cm – m-scale, medium-gray to grayish-black limestones and marlstones with TOC up to ~4%. ^ The results indicate that the lowest 85 m of the section, from latest Barremian -earliest Aptian, characterize a deepening phase of the basin concomitant with sustained riverine flux and intensified primary productivity. These changes induced a shift in the sedimentation pattern and decreased the oxygen levels in the water column through organic matter respiration and limited ventilation of the basin. ^ The upper 155 m comprising the earliest – late-early Aptian document the occurrence of OAE1a and its associated geochemical signatures (TOC up to 3% and a positive shift in δ13C of ~5‰). However, a low enrichment of redox-sensitive trace elements indicates that the basin did not achieve anoxic conditions. The results also suggest that a shallower-phase of the basin, coeval with platform progradation, may have increased ventilation of the basin at the same time that heightened sedimentation rates and additional input of organic matter from terrestrial sources increased the burial and preservation rate of TOC in the sediment.^

Morningness-eveningness and sociosexuality: Evening females are less restricted than morning ones

Sociosexual orientation is a construct describing the propensity to engage in casual sex and sexual activity in uncommitted relationships, varying from restricted to unrestricted orientation. The personality profile of people exhibiting unrestricted sociosexuality matches a personality profile related to eveningness. Previous research on sociosexuality and morningness–eveningness is scarce, however, and conducted only with male participants. The present study aimed at testing whether eveningness is related to unrestricted sociosexuality in both genders. Participants were 352 (62.8% female) Poles aged between 17 and 57. They completed the reduced morningness–eveningness Questionnaire and the revised Sociosexual Orientation Inventory, consisting of three facets: behavior, attitude, and desire. The results revealed that females were more restricted than males in all facets of sociosexuality. Moreover, in both genders older age was related to less restricted behavior and attitude. Analyses showed that morningness– eveningness was unrelated to sociosexuality in males, but in females eveningness was linked to less restricted global sociosexuality .Eveningness in females could be regarded as a contributory factor to the instability of romantic relationships and high-risk sexual behaviors.