Darbe nagrinėjamas begalinio indekso homogeninis kraštinis Rymano uždavinys, kurio laipsninė eilė yra 0<ρ<1. Kiekvienoje iš klasių B ir B(ρ) ieškomas sprendinys - dalimis analizinė funkcija, kai jos ribinės reikšmės realiosios ašies taškuose tenkina kraštinę sąlygą. Darbe tiriamas šio uždavinio išsprendžiamumas ypatinguoju atveju pusplokštumei, ieškomos funkcijos, kurios analizinės viršutinėje ir apatinėje pusplokštumėse. Nagrinėjama koeficiento G(t) nulių ir polių, bei koeficiento modulio augimo įtaka uždavinio išsprendžiamumui. Taip pat tiriama priklausomybė tarp duotųjų dydžių, kuriems esant kraštinis Rymano uždavinys aprėžtų sprendinių neturi. Be to sudarytas bendrasis sprendinys, išskiriant atvejus, kai uždavinys neišsprendžiamas šiose klasėse. / This paper analyses homogeneous boundary-value problem of Riemann with the infinite index, when gradual order is 0<ρ<1. In every class - B and B(ρ) - the solution is partial analitic function, when its limit values meet the marginal condition in the points of real axis. The paper also discusses solvability of the problem in the special case for the half – plane. Moreover, functions are examinated, of which analytic upside and underside half-plane. The coefficient‘s zero and piles are analyzed as possible influential factors for the problem’s solvalibility. The paper examines dependence between given variables for which boundary-value problem of Riemann does not have limited solutions. Furthermore, general solution is presented, excluding cases when the problem is unsolvable in these classes.

Loneliness, unhappiness, and discord pervade David Foster Wallace’s novel Infinite Jest. Parental neglect and abuse, drug and alcohol addiction, and obsession with entertainment all work to increase characters’ narcissism and self-absorption. This increased narcissism prevents characters from developing meaningful relationships, and this absence of meaningful relationships contributes to the feeling of sadness that plagues the Organization of North American Nations. Rather than confronting reality and working to overcome their sadness by attempting to form meaningful relationships, characters instead seek to escape this sadness through the various fantasies provided by drug-use and entertainment. These fantasies only work to exacerbate characters’ self-absorption and narcissism which consequently increases their unhappiness. Certain characters are able to break free of these narcissistic impulses by turning outwards to form meaningful relationships. As these characters break free of the “cage of the self” (777), they experience a sense of meaning and happiness that other characters are without. / iv, 114 leaves ; 29 cm

We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.

Element test results reported in the literature under both triaxial and plane strain conditions indicate that loose saturated granular specimens can experience softening instability at stress ratios lower than what might otherwise be expected given the critical state friction angle of the soil. The region of potential softening instability in stress-space is often explained using the framework of the instability line. This phenomenon is particularly relevant to shallow slopes of 1 to 2 m depth. However, the practical realities of sample preparation for triaxial testing make performing tests below 20 to 30 kPa of confining stress exceptionally difficult. In this thesis, the development of a centrifuge tilt-table test device is described which aims to test the behaviour of loose granular slopes under stress paths of increasing slope inclination or increasing pore water pressure. A system of instrumentation including pore pressure transducers, inclinometers, displacement transducers, and high-resolution cameras was designed to monitor the behaviour of the slope model. The development of a system to provide a controlled groundwater level within the slope model proved to be particularly challenging. The results of two competing design concepts are presented for the water boundary condition and discussed. The centrifuge tilt-table is used to compare the physical response of a slope to the behaviour predicted by the infinite slope and softening instability models using scale model centrifuge testing. If softening instability is a rigorous concept, it should be the primary observed failure mechanism as it will occur at a stress state below the failure line. Tests were performed on loose Ottawa F110 sand at 1g, 20g and 40g and 60g. Deviatoric strain-softening was observed in loose dry sand. The softening instability event resulted in a rapid increase in shear strain at constant shear stress while the soil was at a stress state below the failure envelope. Any soil that can experience softening instability (i.e. granular, loose, saturated, and behaves undrained) will undergo two failures: one caused by deviatoric strain-softening (softening instability) and a second caused by shear failure at a larger slope angle. / Thesis (Master, Civil Engineering) -- Queen's University, 2014-04-29 22:01:36.786

Thesis (M. Sc.)--Carleton University, 2005. / Includes bibliographical references (p. 111-114). Also available in electronic format on the Internet.

Thesis (Ph.D.) -- Mississippi State University. Department of Mathematics and Statistics. / Title from title screen. Includes bibliographical references.

Μελετάμε την έννοια του άπειρου γινομένου μιγαδικών αριθμών και τη συσχέτισή τους με τις άπειρες σειρές. Στη συνέχεια μελετάμε το θεώρημα παραγοντοποίησης του Weierstrass καθώς και το Θεώρημα Mittag-Leffler. / We study the concept of the infinite products and their relationship with the infinite series. We also study Weierstrass' Approximation Theorem and also Mittag-Leffler's Theorem.

The Thompson groups $F, T$ and $V$ are important groups in geometric group theory: $T$ and $V$ being the first discovered examples of finitely presented infinite simple groups. There are many generalisations of these groups including, for $n$ and $r$ natural numbers and $1 < r < n$, the groups $F_{n}$, $T_{n,r}$ and $G_{n,r}$ ($T ≅ T_{2,1}$ and $V ≅ G_{2,1}$). Automorphisms of $F$ and $T$ were characterised in the seminal paper of Brin ([16]) and, later on, Brin and Guzman ([17]) investigate automorphisms of $T_{n, n-1}$ and $F_{n}$ for $n > 2$. However, their techniques give no information about automorphisms of $G_{n,r}$. The second chapter of this thesis is dedicated to characterising the automorphisms of $G_{n,r}$. Presenting results of the author's article [10], we show that automorphisms of $G_{n,r}$ are homeomorphisms of Cantor space induced by transducers (finite state machines) which satisfy a strong synchronizing condition. In the rest of Chapter 2 and early sections of Chapter 3 we investigate the group $\out{G_{n,r}}$ of outer automorphisms of $G_{n,r}$. Presenting results of the forthcoming article [6] of the author's, we show that there is a subgroup $\hn{n}$ of $\out{G_{n,r}}$, independent of $r$, which is isomorphic to the group of automorphisms of the one-sided shift dynamical system. Most of Chapter 3 is devoted to the order problem in $\hn{n}$ and is based on [44]. We give necessary and sufficient conditions for an element of $\hn{n}$ to have finite order, although these do not yield a decision procedure. Given an automorphism $\phi$ of a group $G$, two elements $f, g ∈ G$ are said to be $\phi$-twisted conjugate to one another if for some $h ∈ G$, $g = h−1 f (h)\phi$. This defines an equivalence relation on $G$ and $G$ is said to have the $\rfty$ property if it has infinitely many $\phi$-twisted conjugacy classes for all automorphisms $\phi ∈ \aut{G}$. In the final chapter we show, using the description of $\aut{G_{n,r}}$, that for certain automorphisms, $G_{n,r}$ has infinitely many twisted conjugacy classes. We also show that for certain $\phi ∈ \aut{G_{2,1}}$ the problem of deciding when two elements of $G_{2,1}$ are $\phi$-twisted conjugate to one another is soluble.

This thesis is conceived as a learning text, which deals with infinite numerical series. The thesis thematicaly results from curriculum for lectures of fourth therm's analysis for field called "Pedagogy of mathematics for secondary schools" on Pedagogical faculty by University of South Bohemia. It contains theoretical interpretation of basic concepts and theorems about infinite series, including of proofs of shown theorems, plenty of solved excersises, which show aplication of these concepts and theorems, and collection of excercises to study indipendently as well.

viii, 133 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / In this dissertation, we will study the crossed product C*-algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable recursive subhomogeneous algebras (SRSHAs), which differ from recursive subhomogeneous algebras introduced by N. C. Phillips in that the irreducible representations of SRSHAs are infinite dimensional instead of finite dimensional. We show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and non-vanishing have topological stable rank one. We then construct C*-subalgebras of the crossed product that are analogous to the C*-subalgebras in the studies of free minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. Finally, we prove that these C*-algebras are in fact simple inductive limits of SRSHAs in which the connecting maps are injective and non-vanishing. Thus these C*-subalgebras have topological stable rank one. / Committee in charge: Christopher Phillips, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Huaxin Lin, Member, Mathematics; Yuan Xu, Member, Mathematics; Dietrich Belitz, Outside Member, Physics