Academic literature on the topic 'Relations (general) with Ingria (R.S.F.S.R.)'

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, ?, f, p]0 (?r, E), [V, ?, f, p]1 (?r, E), [V, ?, f, p]? (?r, E) S? (?r, E) and S?0 (?r, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space S? (?r, E) may be represented as a [V, ?, f, p]1 (?r, E)space.

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

The purpose of this paper is to introduce the space of sequences that are ?r-strongly almost summable with respect to a modulus function. We give some relations related to these sequence spaces. We also show that the space s(?r)of ?r-almost statistically convergent sequences may be represented as a [c,f] (?r)space.

Let S be the family of functions f(z) = z + a2z2 + … which are analytic and univalent in |z| < 1. We find the valueas a function of r 0 < r < 1. The known lower estimate ofis improved. Relations with the growth theorem are considered and the radius of univalence of f(z)/z is discussed.

An H-relation, as introduced by Rossa and Tangeman [4], is a relation σ on the class of associative rings with their subrings satisfying the following conditions:(1) IσR implies that I is a subring of R;(2) if IσR and f is a homomorphism of R, then (If)σ(Rf);(3) if IσR and J is an ideal of R, then (I∩J)σJ.Puczylowski [3] imposes also the condition(4) if J is an ideal of R, then JσR.A further condition satisfied by many familiar H-relations is the following:(5) if f is a homomorphism from a ring R onto a ring S and BσS, then there exists a subring A of R such that AσR and Af = B.

AbstractThe problem of finding a nontrivial factor of a polynomial$f(x)$over a finite field${\mathbb{F}}_q$has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the generalized Riemann hypothesis (GRH). In this work we improve the state of the art by focusing on prime degree polynomials; let$n$be the degree. If$(n-1)$has a ‘large’$r$-smooth divisor$s$, then we find a nontrivial factor of$f(x)$in deterministic$\mbox{poly}(n^r,\log q)$time, assuming GRH and that$s=\Omega (\sqrt{n/2^r})$. Thus, for$r=O(1)$our algorithm is polynomial time. Further, for$r=\Omega (\log \log n)$there are infinitely many prime degrees$n$for which our algorithm is applicable and better than the best known, assuming GRH. Our methods build on the algebraic-combinatorial framework of$m$-schemes initiated by Ivanyos, Karpinski and Saxena (ISSAC 2009). We show that the$m$-scheme on$n$points, implicitly appearing in our factoring algorithm, has an exceptional structure, leading us to the improved time complexity. Our structure theorem proves the existence of small intersection numbers in any association scheme that has many relations, and roughly equal valencies and indistinguishing numbers.

An investigation is carried out to consider a renormalized HVT approach in the context of s-power series expansions for the energy eigenvalues of a particle moving non-relativistically in a central potential well belonging to the class V(r)=−Df(rR), D>0 where f is an appropriate even function of x=r/R and the dimensionless quantity s = (h^2/2μDR)^{1/2} is assumed to be sufficiently small. Previously, the more general class of central potentials of even power series in r is considered and the renormalized recurrence relations from which the expansions of the energy eigenvalues follow, are derived. The s-power series of the renormalized expansion are then given for the initial class of potentials up to third order in s (included) for each energy-level Enl . It is shown that the renormalization parameter Κ enters the coefficients of the renormalized expansion through the state-dependent quantity a_{nl}χ^{1/2} =a_{nl}(1+K ((−d_1D)R^2))^{½}, a_{nl}=(2n+l+32). The question of determining χ is discussed. Our first numerical results are also given and the utility of potentials of the class considered (to which belong the well-known Gaussian and reduced Poschl- Teller potentials) in the study of single–particle states of a Λ in hypernuclei is pointed out.

The investigation is in the Constructive algebra in the sense of E. Bishop, F. Richman, W. Ruitenburg, D. van Dalen and A. S. Troelstra. Algebraic structures with apartness the first were defined and studied by A. Heyting. After that, some authors studied algebraic structures in constructive mathematics as for example: D. van Dalen, E. Bishop, P. T. Johnstone, A. Heyting, R. Mines, J. C. Mulvey, F. Richman, D. A. Romano, W. Ruitenburg and A. Troelstra. This paper is one of articles in their the author tries to investigate semugroups with apartnesses. Relation q on S is a coequality relation on S if it is consistent, symmetric and cotran-sitive; coequality relation is generalization of apatness. The main subject of this consideration are characterizations of some coequality relations on semigroup S with apartness by means od special ideals J(a) = {x E S : a# SxS}, principal consistent subsets C(a) = {x E S : x# SaS} (a E S) of S and by filled product of relations on S. Let S = (S, =, 1) be a semigroup with apartness. As preliminaries we will introduce some special notions, notations and results in set theory, commutative ring theory and semigroup theory in constructive mathematics and we will give proofs of several general theorems in semigroup theory. In the next section we will introduce relation s on S by (x, y) E s iff y E C(x) and we will describe internal filfulments c(s U s?1) and c(s ? s?1) and their classes A(a) = ?An(a) and K(a) = ?Kn(a) respectively. We will give the proof that the set K(a) is maximal strongly extensional consistent ideal of S for every a in S. Before that, we will analyze semigroup S with relation q = c(s U s?1 ) in two special cases: (i) the relation q is a band coequality relation on S : (ii) q is left zero band coequality relation on S. Beside that, we will introduce several compatible equality and coequality relations on S by sets A(a), An(a), K(a) and Kn(a).

1. The effects of excitatory postsynaptic potentials (EPSPs) on interspike intervals (ISIs) of neocortical neurons can be mimicked by pulse potentials (PPs) produced by current injection. The present report documents the dependence of the ISI shortening on the amplitudes of PPs and EPSPs and on the firing rate of the affected neuron. 2. In rhythmically firing necortical neurons, the ISI shortenings caused by PPs arriving at specific times in the ISI can be described by a shortening-delay (S-D) curve. The S-D curve yields three measures of the PPs' ability to shorten the ISI: 1) the mean ISI shortening, S; 2) the maximum shortening, Smax; and 3) the effective interval, defined as the portion of the ISI in which the PP consistently shortens the ISI. For PPs ranging between 80 microV and 3.6 mV (and cells firing at 25 imp/s), the mean shortening increased with amplitude h as S (ms) = 1.2*h (mV)1.24 (r = 0.94; P < 0.01). Smax increased linearly with amplitude as 4.9 ms/mV (r = 0.86, P < 0.01). The effective interval (as a percentage of the ISI) increased slightly with PP amplitude and had a mean value of 65 +/- 21% (mean +/- SD). 3. S-D curves obtained with stimulus-evoked EPSPs varied with EPSP amplitude in a manner similar to those of PPs. The relations obtained for stimulus-evoked EPSPs were not statistically different from those obtained for PPs in the same cells. 4. To determine the effect of firing rate. PPs were applied while neurons fired at frequencies ranging from 8 to 71 imp/s. Both S and Smax were approximately inversely proportional to the baseline firing rate (fo) and could be described as: S or Smax = kfo-m. The mean value of the exponent m (+/- SD) was 0.96 +/- 0.25 for S and 1.2 +/- 0.4 for Smax. These values were not statistically different from a value of 1 (1 group, 2-tailed t test). The effective interval did not vary significantly with firing rate. 5. The dependence of S on PP amplitude and baseline firing rate was incorporated into an expression for the average change in firing rate (delta f) produced by PPs occurring at rate fs: delta f = 0.03 h1.24 fs. The delta f increased with PP amplitude but did not vary significantly with the baseline firing rate. The values of delta f calculated from the S-D curves matched the values that were computed directly from the spike trains.(ABSTRACT TRUNCATED AT 400 WORDS)

Background:Dryness, fatigue, and pain are common clinical manifestations assessed by EULAR Sjogren’s Syndrome Patient Reported Index (ESSPRI)-Dryness, -Fatigue, -Pain scores in patients with primary Sjögren’s syndrome (pSS). In addition, depression is also seen in these patients owing to the pattern of the chronic disease.Objectives:The aim of the study was to assess the complex interactions among Depression status, Illness Perception, and prominent clinical manifestations evaluated by the ESSPRI (Dryness, Fatigue, and Pain) in patients with pSS.Methods:In this cross-sectional study, 111 patients with pSS (M/F: 5/106; mean age: 52.9 ± 12.01 years) were included. The data were collected by clinical examination and a questionnaire regarding patient reported outcome measures (PROMs). Unstimulated (U-WSFR) and stimulated (S-WSFR) whole saliva flow rates of patients were calculated as ml/min. Hospital Anxiety and Depression Scale (HADS), Illness Perception Questionnaire-R (IPQ-R) and EULAR Sjogren’s Syndrome Patient Reported Index were filled by patients. Increases in HADS score and subgroup scores of ESSPRI (Dryness, Fatigue and Pain) and IPQ-R dimensions regarding Identity, Consequences, and Emotional reflected poor conditions for patients. In addition, patients scored their disease activity (0: inactive-100: the worst activity) by using 100-mm visual analogue scale (VAS). After preliminary analysis, a mediation analysis was used to evaluate the relations among these variables.Results:In the study, ESSPRI-Dryness score (6,27±2,79) was associated with U-WSFR (0,40±0,57) and S-WSFR (1,04±0,86),(r:-0,4 p=0.000; r:-0,3 p=0.004). Moreover, patients reported disease activity score (48,78±26,67) was related to U-WSFR (r: -0,3 p=0.026) as well as Consequence (19,12±5,47) and Emotional (19,54±7,02) scores of IPQ-R questionnaire (r: 0,3 p=0.035; r: 0,3 p=0.014).In IPQ-R questionnaire, Identity score (8,04±3,1) reflecting number of symptoms that patients experienced due to their illness was correlated with scores of ESSPRI-Fatigue (5,29±2,97), ESSPRI-Pain (5,18±3,01), HADS-Anxiety (11,67±5,55), HADS-Depression (9,2±4,98) in the study (p<0.05).In the mediation analysis, Identity score was directly mediated by ESSPRI-Fatigue score (p=0.0093) and indirectly mediated by HADS-Depression score (p=0.0011).A bootstrap analysis with 5000 replications was applied to estimate mediation effect to generate 95% CI. Percentile bootstrap of HADS-Depression was found to be an effective mediator for Identity score based on 5000 bootstrap sample.Conclusion:Both depression status and fatigue affected Identity score reflecting the number of symptoms poorly. Considering this complex relationship in disease activity assessment may positively affect disease outcomes.Disclosure of Interests:None declared

This unusual book explores the historical assumptions at work in the style of literary criticism that came to dominate English studies in the twentieth century. Stefan Collini shows how the work of critics renowned for their close attention to ‘the words on the page’ was in practice bound up with claims about the nature and direction of historical change, the interpretation of the national past, and the scholarship of earlier historians. Among the major figures examined in detail are T. S. Eliot, F. R. Leavis, William Empson, and Raymond Williams, while there are also original discussions of such figures as Basil Willey, L. C. Knights, Q. D. Leavis, and Richard Hoggart. In the period between Eliot’s The Sacred Wood and Williams’s The Long Revolution, the writings of such critics came to occupy the cultural space left by academic history’s retreat into specialized, archive-bound monographs. Their work challenged the assumptions of the Whig interpretation of English history and entailed a revision of the traditional relations between ‘literary history’ and ‘general history’. Combining close textual analysis with wide-ranging intellectual history, this book both revises the standard story of the history of literary criticism and illuminates a central feature of the cultural history of twentieth-century Britain.

First-order logic is a richer language than propositional logic. Its lexicon contains not only the symbols ∧, ∨, ￢, →, and ↔ (and parentheses) from propositional logic, but also the symbols ∃ and ∀ for “there exists” and “for all,” along with various symbols to represent variables, constants, functions, and relations. These symbols are grouped into five categories. • Variables. Lower case letters from the end of the alphabet (. . . x, y, z) are used to denote variables. Variables represent arbitrary elements of an underlying set. This, in fact, is what “first-order” refers to. Variables that represent sets of elements are called second-order. Second-order logic, discussed in Chapter 9, is distinguished by the inclusion of such variables. • Constants. Lower case letters from the beginning of the alphabet (a, b, c, . . .) are usually used to denote constants. A constant represents a specific element of an underlying set. • Functions. The lower case letters f, g, and h are commonly used to denote functions. The arguments may be parenthetically listed following the function symbol as f(x1, x2, . . . , xn). First-order logic has symbols for functions of any number of variables. If f is a function of one, two, or three variables, then it is called unary, binary, or ternary, respectively. In general, a function of n variables is called n-ary and n is referred to as the arity of the function. • Relations. Capital letters, especially P, Q, R, and S, are used to denote relations. As with functions, each relation has an associated arity. We have an infinite number of each of these four types of symbols at our disposal. Since there are only finitely many letters, subscripts are used to accomplish this infinitude. For example, x1, x2, x3, . . . are often used to denote variables. Of course, we can use any symbol we want in first-order logic. Ascribing the letters of the alphabet in the above manner is a convenient convention. If you turn to a random page in this book and see “R(a, x, y),” you can safely assume that R is a ternary relation, x and y are variables, and a is a constant.