# Top PDF A note on the proof of Bertrand's theorem

### A note on the proof of Bertrand's theorem

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]

### Fermat’s Last Theorem over Number Fields

The proof of FLT is based on three main pillars: Mazur’s irreducibility theorem, Wiles’ modularity theorem for semistable elliptic curves over Q and Ribet’s level lowering theorem. Explaining these pillars will involve a detour into some of the most fascinating areas of modern number theory: elliptic curves, Galois representations, modular forms and modularity. For a comprehensive introduction to these topics we suggest [3, 21, 22]. For an overview and history of various methods to study the Generalized Fermat equation x r + y q = z p we refer to [1], which we follow closely in this section.
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### REPOSITORIO INSTITUCIONAL DA UFOP: A Note on a theorem of Guo, Mezo, and Qi.

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.

### On the groups satisfying the converse of Schur's theorem

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

### A note on an application of Arrow's theorem: sufficient conditions for Lucas' inflation and welfare

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]

### On the existence of complete bounded minimal surfaces in RN

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]

### Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems

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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### SOCIAL ECONOMY – A FORM OF INCLUSION AND OF ''REACTIVATING'' OF LABOR IN THE CONTEXT OF THE CURRENT CRISIS

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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### On the Stability of Volterra Difference Equations of Convolution Type

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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### Weighted Sobolev theorem in Lebesgue spaces with variable exponent

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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### Effect of heat treatment parameters on the properties of low-alloy cast steel with microadditions of vanadium

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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### Interpreting a Classical Geometric Proof with Interactive Realizability

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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### Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup

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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### A Method To Find The Area Of Sector Without The Usage Of Angle Made By The Chord

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.

### On Deformation of Foliations with a Center in the Projective Space

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.

### Prostate Cancer: A State of The Heart

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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### Note on an (s, S) Inventory System with Decay

The limiting distribution of I(t) as t → ∞ exists, since {I(t)} is a bounded Markov process. Let F (x), x ≤ S, denote the steady-state cdf; f(x) = dF (x) dx , s < x < S, is the pdf, wherever the derivative ex- ists. We assume the decay rate is r(x) = kx > 0, x ∈ (s, S]. This choice of r(x) results in a negative expo- nential decay pattern for the sample path, and gen- eralizes the hs, Si model with constant decay rate (e.g., [1], [3]). We illustrate the solution technique by taking ¯ B(x) = e −μx , x > 0, μ > 0.
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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

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]