theorem present both the in Bertrand's original paper Théorème relatif au.. movement d'un point attiré vers un entre xe and in the Arnold's book Math-.[r]

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In a recent paper, Guo, Mez˝ o, and Qi proved an identity representing **the** Bernoulli polynomials at non-negative integer points m in terms **of** **the** m-Stirling numbers **of** **the** second kind. In this **note**, using a new representation **of** **the** Bernoulli polynomials in **the** context **of** **the** Zeon algebra, we give an alternative **proof** **of** **the** aforementioned identity.

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by some function B **of** n (by a capable group, we mean a group G which can be occurred as **the** group **of** inner automorphisms **of** some group E). Indeed he defined **the** relevant function B(n) recursively. But one should **note** that **the** definition **of** B was not explicit. In 2005, Podoski and Szegedy [11] tried to improve **the** Isaac’s result in such a way that with a weaker condition, they could attain a better conclusion. They actually proved

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We are interested in finding the conditions under which the (unique) stationary point (m, X) satisfying the conditions of the Arrow theorem, and characterized by the f[r]

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Theorem. There is no complete minimalsurface with bounded curvature immer.sed in R+. The proof involves the use of Herglotz's theorem on the boundary behaviour of po[r]

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We begin by introducing fundamental notions for **the** study **of** cohomology in dynamical systems (Section 2.1). In particular, we introduce **the** concepts **of** cocycle, coboundary and cohomology between cocycles. We present cohomological equations in **the** case **of** continuous time and discuss **the** fundamental relationship between **the** existence **of** solutions **of** these equations and **the** behavior **of** **the** cocycles along periodic orbits (Section 2.2). We will go **on** by presenting a detailed **proof** **of** **the** Livschitz **Theorem** in a version for hyperbolic flows (Section 3), and then discuss **the** generalization **of** this **Theorem** to suspension flows (Section 4). This generalization allows an alternative **proof** **of** **the** Livschitz **Theorem** for hyperbolic flows based **on** Bowen and Ratner’s construction **of** Markov systems for (hyperbolic) flows [3,4]. As far as is known, these last two approaches are new (Section 5).

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than they produce, which means over **the** real incomes obtained through social work. Văduva, . We are talking about New Zeeland. Most countries present important sovereign debts , an increasing deficit between incomes and expenses, practical risks **of** making new loans that bring them close to **the** insolvency area or to bankruptcy **The** European Commission, . Such a process is explained by **the** confusion between **the** exigencies **of** social economy – based **on** work – and **the** passive social protection policies, which ignore or place labor between brackets . )nstead **of** **the** minimum guaranteed salary, some irrational social policies have promoted **the** minimum guaranteed income, independent from **the** work resources **of** **the** beneficiaries, poverty is perceived as a state characterizing **the** majority Vîrjan , p. . Successes, but also limits recorded in **the** labor market today are similar to those defining **the** reform **of** **the** Romanian economy as a whole Aceleanu and Cretu , p. , marked by a public‐private partnership are organizationally weak and frail, **the** tensions between labor market structures and mechanisms that interfere with legislative‐institutional tensions.

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Therefore, if R = 1, **the** validity **of** **theorem** 2 is an open problem since **the** analyticity **on** **the** unit circumference can not be applied. Besides **theorem** 4, some other results give us some sufficient conditions for **the** asymptotic stability **of** **the** null solution **of** (1.1) and can be found in [1, 7, 11, 9, 2, 14, 12, 13].

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In **the** weighted theory, Sobolev embeddings were obtained for power weights. First, for bounded domains there was obtained **the** weighted p( ·) → p(·)-boundedness in V. Koki- lashvili and **S**. Samko [11] and **the** p( ·) → q(·)-inequality with **the** limiting exponent q(·) in **S**. Samko [26]. As is known, **the** case **of** unbounded domains is more difficult (when p( ·) is al- lowed to be variable up to infinity). A generalization **of** **the** Stein–Weiss inequality [26], that is, Sobolev embedding with power weight **on** unbounded domains for variable exponents was con- sidered in [24], where this generalization was obtained with a certain additional restriction **on** **the** parameters involved. This restriction was withdrawn in [25]. **The** progress in [24,25] became possible under **the** log-condition **on** **the** variable exponent at infinity, a little bit stronger than **the** decay condition.

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This article examines **the** effect **of** prolonged time **of** holding at **the** temperature **of** 620 0 C **on** **the** processes **of** secondary phase precipitation and mechanical properties **of** low-alloy cast steel with an addition **of** vanadium subjected to two variants **of** heat treatment, i.e. U:1150 0 C+H:950 0 C+O:620 0 C and H:950 0 C+O:620 0 C. To determine an impact **of** **the** applied heat treatment operations, testing **of** mechanical properties and microstructural examinations **of** **the** cast steel with 0,21 and 0,27%C were carried out.

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This is very different from what one could expect by a superficial look at **the** **proof** **of** Lemma 3. Indeed, if **the** order **on** **the** reals were decidable, then this simple and natural **proof** would be quite efficient, since its complexity would be linear in n. However, its interactive interpretation has exponential complexity. This can be seen in **the** computation tree too: a single computation corresponds to a path and paths have length n. **On** **the** other hand, since we have backtracking, in **the** worst case we may have to perform every possible computation. Naturally, since **the** order **on** **the** reals is undecidable, an actual comparison is impossible.

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In **the** case **of** constant p it was also known that **the** Bessel potential space B α [ L p ( ·) (R n )] may be characterized in terms **of** **the** rate **of** convergence **of** identity approximations. For instance, with **the** usage **of** **the** Poisson semigroup P t , t > 0, **the** space B α [ L p ( R n ) ] is described as **the** subspace **of** L p ( R n ) **of** functions f for which there exists **the** limit lim t → 0 t 1 α ( I − P t ) α f , besides this

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As we know that to find **the** area **of** sector **the** angle made by **the** chord (that is chord which divides **the** circle) is required. But in **the** below method we find **the** ratio **of** **the** segments **of** **the** circle. Thus by relating **the** area **of** segment to **the** area **of** sector **the** area **of** sector could be found. **The** ratio **of** area **of** segments is related to tangents that are drawn through diameter **on** either side.

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This **theorem** also says that **the** persistence **of** one center along **the** deformation implies **the** persistence **of** all other centers and radials. J.R. Muciño in (Muciño 1995) has also studied this problem in **the** case p = q = 1. However, he has not obtained **the** result **of** **Theorem** 1 in this case, as we will explain later in §2.

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Prof Alberto Briganti’s presentation began with **the** case **of** a 57-year-old male diagnosed with a 4 + 3 bilateral extended prostate cancer. **The** patient displayed some CV risk factors, including diabetes and obesity. Following staging, **the** patient appeared to have no systemic disease in **the** bone or in **the** abdomen and pelvis; however, a prostate magnetic resonance imaging (MRI) scan showed a suspicious area **of** minimal extracapsular extension at **the** right apex. Prostate-speciic antigen (PSA) levels were 21.6 ng/mL, indicating that he was a high-risk patient. He consequently underwent bilateral extended pelvic lymph node dissection (PLND). **The** inal pathological report revealed that **the** patient had a Gleason score **of** 8, 2/21 positive lymph nodes, and a positive surgical margin, with complete recovery **of** urinary continence at 4 weeks after surgery. Post-surgery evaluation showed that **the** patient had a PSA **of** 0.07 ng/mL, had no spontaneous erections, and did not require a protective pad at 40 days.

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Corrections to the paper “Sharp estimates of the growth of the Poisson-Stieltjes integral in the polydisc” by I.E.Chyzhykov, O.A.Zolota.. The proof of the sufficiency of the theorem in [[r]

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Relative advantage is defined as **the** extent to which a person views an innovation as offering an advantage over previous ways **of** performing **the** same task (Roger, 1983; Agarwal & Prasad, 1997). Because Internet banking services allow customers to access their banking account from any location 24 hours a day and 7 days a week, it provides an enormous advantage and convenience to users (Tan & Teo, 2000). It also gives customers greater control over managing their finances, as they are able to check their accounts easily. Besides, a customer’s Internet experience, his or her banking needs can affect his adoption. As there are more financial products and services, it is expected that individuals with many financial accounts and who subscribe to many banking services will be more inclined to adopt Internet banking. Tan and Teo (2000) has reported that potential adopters **of** Internet banking services are likely to own multiple banking accounts and subscribe to various banking services. Rogers argues that potential adapters, who are allowed to experiment with an innovation will feel more comfortable with **the** innovation and are more likely to adopt it. Thus, if customers have **the** opportunity to try **the** innovation, certain fears **of** **the** unknown may be minimized. Government policy could also aid or hinder Internet diffusion (Mbarika, 2002). This is consistent with **the** national systems **of** innovation theory that posits that government policies may encourage or mandate technology development and adoption (King et. al., 1994; Wolcott et. al., 2001). Tan and Teo (2000) suggest that **the** greater **the** extent **of** government support for Internet commerce, **the** more likely Internet banking will be adopted, thus, confirming Goh’s (1995) suggestion that governments can play an interventionist and leading role in **the** diffusion **of** innovation. Potential users in turn would view new applications such as Internet banking services more favorably and hence be more like to use them. Thus, **the** second alternative hypothesis is:

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