Theorem Arguments Research Articles

The compactly supported wavelet characterization of non-homogeneous Herz-Sobolev spaces with variable exponent

Our aim in the present paper is to introduce non-homogeneous Herz-Sobolev spaces with variable exponent and to obtain a wavelet characterization and an unconditional basis of them using wavelets with proper decay and compact support. Our method is based on the extrapolation theorem and duality argument.

Chain Length Determines the Folding Rates of RNA

We show that the folding rates (kFs) of RNA are determined by N, the number of nucleotides. By assuming that the distribution of free-energy barriers separating the folded and the unfolded states is Gaussian, which follows from central limit theorem arguments and polymer physics concepts, we show that kF≈k0exp(−αN0.5). Remarkably, the theory fits experimental rates spanning over 7 orders of magnitude with k0∼1.0(μs)−1. Our finding suggests that the speed limit of RNA folding is ∼1 ms, just as it is in the folding of globular proteins.

An introduction to complex analysis

Part 1 The complex plane: complex numbers open and closed sets in the complex plane limits and continuity. Part 2 Holomorphic function and power series: complex power series elementary functions. Part 3 Prelude to Cauchy's theorem: paths integration along paths connectedness and simple connectedness properties of paths and contours. Part 4 Cauchy's theorem: Cauchy's theorem, level I and II logarithms, argument and index Cauchy's theorem revisited. Part 5 Consequences of Cauchy's theorem: Cauchy's formulae power series representation zeros of holomorphic functions the maximum-modulus theorem. Part 6 Singularities and multifunctions: Laurent's theorem singularities meromorphic functions multifunctions. Part 7 Cauchy's residue theorem: counting zeroes and poles claculation of residues estimation of integrals. Part 8 Applications of contour integration: improper and principal-values integrals integrals involving functions with a finite number of poles and infinitely many poles deductions from known integrals integrals involving multifunctions evaluation of definite integrals. Part 9 Fourier and Laplace tranforms: the Laplace tranform - basic properties and evaluation the inversion of Laplace tranforms the Fourier tranform applications to differential equations proofs of the Inversion and Convolution theorems. Part 10 Conformal mapping and harmonic functions: circles and lines revisited conformal mapping mobius tranformations other mappings - powers, exponentials, and the Joukowski transformation examples on building conformal mappings holomorphic mappings - some theory harmonic functions.

What factors motivate the analysts’ stock recommendation in a small emerging market? Evidence from Sri Lanka

The purpose of this research is to determine the criteria used by the analysts for stock recommendation, identification of certain key factors which are useful for individual investors. According to the Modigliani-Miller theorem, the factors which affect dividend and capital gain could also influence investors. The regression analysis was used to identify the factors which influence the analysts’ stock recommendations. The P/E ratio, dividend yield, return on equity and rate of retained profit are the financial indicators which affected analysts’ advice. The market performance indicators of the return sort, volatility of shares have a significant impact on perfect investment decision. The emerging markets exhibit greater sensitivity to abnormal volume trading. However, we found that it is less sensitive to stock analysts’ recommendation in emerging Colombo Security Exchange (CSE). The stock analysts’ recommends more concern on firm dividend than capital gain. We fundamentally disagree with the argument of Modigliani-Miller theorem in terms of analysts’ stock recommendation and individual investor’s point of view. Behavior of individual investors in emerging CSE is preferred on low risk stable dividend than future capital gains. Key words: Colombo Stock Exchange (CSE), stock analyst, individual investors, financial, risk, market.

Interaction regimes for oppositely charged plates with multivalent counterions

Within a mean-field treatment of the interaction between two oppositely charged plates in a salt-free solution, the distance at which a transition from an attractive to a repulsive regime appears can be computed analytically. The mean-field description, however, breaks down under strong Coulombic couplings, which can be achieved at room temperature with multivalent counterions and highly charged surfaces. Making use of the contact theorem and simple physical arguments, we propose explicit expressions for the equation of state in several situations at short distances. The possibility of Bjerrum pair formation is addressed and is shown to have profound consequences on the interactions. To complete the picture, we consider the large-distance limit, from which schematic phase diagram discriminating attractive from repulsive regions can be proposed.

On a class of critical singular quasilinear elliptic problem with indefinite weights

In this paper, the eigenvalue problem for a class of quasilinear elliptic equations involving critical potential and indefinite weights is investigated. We obtain the simplicity, strict monotonicity and isolation of the first eigenvalue λ 1 . Furthermore, because of the isolation of λ 1 , we prove the existence of the second eigenvalue λ 2 . Then, using the Trudinger–Moser inequality, we obtain the existence of a nontrivial weak solution for a class of quasilinear elliptic equations involving critical singularity and indefinite weights in the case of 0 < λ < λ 1 by the Mountain Pass Lemma, and in the case of λ 1 ≤ λ < λ 2 by the Linking Argument Theorem.

Retrospectives: Lionel W. McKenzie and the Proof of the Existence of a Competitive Equilibrium

The theorem proving the existence of general equilibrium in a competitive economy, which necessarily involved specifying the conditions under which such an equilibrium would exist, is an extraordinary achievement of twentieth-century economics. The discovery is commonly attributed to a paper by (eventual) Nobel Prize winners Kenneth Arrow and Gerard Debreau: “Existence of an Equilibrium for a Competitive Economy,” published in the July 1954 issue of Econometrica. However it is less well-known that Lionel McKenzie published a paper in the previous issue of Econometrica, “On Equilibrium in Graham's Model of World Trade and Other Competitive Systems,” that discussed many of the same themes. Both papers established the existence of a competitive equilibrium for suitable general equilibrium models and employed fixed point theorem arguments. McKenzie had priority in publication in 1954 and received credit for simultaneous discovery in prominent sources around that time. But over the years, McKenzie's role in creating the proof of the existence of a general equilibrium seems to have faded from the collective consciousness of the economics profession. Newly available archival material permits a reexamination of the events surrounding the publication of both Econometrica papers in 1954. The story raises general issues concerning “simultaneous discovery,” “priority,” and “credit” in economic research and opens a window into some academic practices of that time.

What Factors Motivate the Stock Analyst Forecast on Listed Companies in Colombo Stock Exchange?

The purpose of this research is to determine the main forecasting factors of stock analysts, to analyze whether stock analysts have a rational base for their advice to the individual investors. According to the Modigliani-Miller theorem, the factors which affected to dividend and capital gain could influence investors. The regression analysis was used to identify the factors which influence the forecast decision on shares of the companies. The P/E ratio, dividend yield, return on equity and rate of retained profit are the financial indicators which affected on experts’ advice. The market performance indicators of the return sort, volatility of shares have a significant impact on perfect investment decision. The emerging markets exhibit greater sensitivity to abnormal volume trading, however, we found that it is less sensitive to stock analysts’ forecast in emerging CSE. The stock analysts forecast decision more concern on firm dividend than capital gain. We fundamentally disagree with the argument of Modigliani-Miller theorem in terms of stock analysts’ forecast and individual investor’s point of view. Because, behavior of individual investors in emerging CSE is prefer on low risk stable dividend than future capital gains. Baker and Powell (1999) and Baker et al. (2001) made same conclusion by studying dividend decision of firms.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Nonstationary homoclinic orbits for an infinite-dimensional Hamiltonian system

We study the following system of diffusion equations on R×RN, ∂tu−Δxu+V(x)u=g(t,x,v), −∂tv−Δxv+V(x)v=f(t,x,u), where z=(u,v):R×RN→R2, V∊C(RN,R), g(t,x,v), f(t,x,u) are periodic in t, x and superlinear at infinity. By a variant linking theorem and concentration compactness arguments, we establish the existence of nonstationary homoclinic-type solutions of least energy for this systems.

Convergence of a nonlinear finite difference scheme for the Kuramoto–Tsuzuki equation

A nonlinear finite difference scheme is studied for solving the Kuramoto–Tsuzuki equation. Because the maximum estimate of the numerical solution can not be obtained directly, it is difficult to prove the stability and convergence of the scheme. In this paper, we introduce the Brouwer-type fixed point theorem and induction argument to prove the unique existence and convergence of the nonlinear scheme. An iterative algorithm is proposed for solving the nonlinear scheme, and its convergence is proved. Based on the iterative algorithm, some linearized schemes are presented. Numerical examples are carried out to verify the correction of the theory analysis. The extrapolation technique is applied to improve the accuracy of the schemes, and some interesting results are obtained.

R&amp;D-Hindering Collusion

Abstract In an extended version of d'Aspremont and Jacquemin's (1988) R&amp;D competition model, we identify a region where the game is a prisoner's dilemma in that region firms' optimal strategy still prescribes to invest in R&amp;D. However, they would obtain a higher profit by not investing at all. A standard Folk Theorem argument suggests that firms implicitly tend to collude and refrain from investing in R&amp;D when their interaction is repeated. When this happens, social welfare shrinks, but we argue that promoting joint research constitutes a remedy to the lack of innovation efforts, rather than the excess thereof.

Stability and Hopf bifurcation for a regulated logistic growth model with discrete and distributed delays

In this paper, we investigate the stability and Hopf bifurcation of a new regulated logistic growth with discrete and distributed delays. By choosing the discrete delay τ as a bifurcation parameter, we prove that the system is locally asymptotically stable in a range of the delay and Hopf bifurcation occurs as τ crosses a critical value. Furthermore, explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by normal form theorem and center manifold argument. Finally, an illustrative example is also given to support the theoretical results.

Arguments for–or against–Probabilism?

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. I discuss the extent to which the original arguments can be buttressed.1. Introduction2. The Dutch Book Argument2.1. Saving the Dutch Book argument2.2. ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’3. Representation Theorem-based Arguments4. The Calibration Argument5. The Gradational Accuracy Argument6. Conclusion

Casimir energy for a double spherical shell: A global mode sum approach

In this work we study the configuration of two perfectly conducting spherical shells. This is a problem of basic importance to make possible development of experimental apparatuses that they make possible to measure the spherical Casimir effect, an open subject. We apply the mode sum method via cutoff exponential function regularization with two independent parameters: one to regularize the infinite order sum of the Bessel functions; other, to regularize the integral that becomes related, due to the argument theorem, with the infinite zero sum of the Bessel functions. We obtain a general expression of the Casimir energy as a quadrature sum. We investigate two immediate limit cases as a consistency test of the expression obtained: that of a spherical shell and that of two parallel plates. In the approximation of a thin spherical shell we obtain an expression that allows to relate our result with that of the proximity-force approximation, supplying a correction to this result.

A note on optimal ordering policies of EOQ model under discount of purchase price or increase of setup cost

The traditional EOQ model assumes that both the setup cost and the purchase cost are independent of the lot size. Matsuyama (2001) modifies the traditional EOQ model such that the setup cost increases as the ordering quantity increases or the purchase cost decreases as the ordering quantity increases. Both Theorem 3 and Corollary 3 in Matsuyama (2001) explore the optimal solution of the average profit per one ordering quantity when the purchase price discount which depends on the ordering quantity. Moreover, both Theorem 5 and Corollary 5 in Matsuyama (2001) determine the optimal solution of the average profit per one ordering quantity when the setup cost which depends on the ordering quantity. Basically, the arguments of Theorem 3, Corollary 3, Theorem 5 and Corollary 5 in Matsuyama (2001) are not complete. Some situations do not be discussed in Matsuyama (2001). Therefore, the main purpose of this paper is to complement the shortcomings of Matsuyama (2001) and to present another alternatives to give complete proofs to Matsuyama (2001). Furthermore, this paper reveals simple solution procedures to find the optimal solutions of the inventory models described in Matsuyama (2001). Finally, numerical examples are used to explain all results obtained by this paper.

Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

We study the initial-boundary value problem for a nonlinear wave equation given by where η ≥ 0, q ≥ 2 are given constants and u 0, u 1, g, k, f are given functions. In this paper, we consider two main parts. In part 1, under a certain local Lipschitzian condition on f with (ũ0, ũ1) ∈ H 1 × L 2; k, g ∈ H 1(0, T), η ≥ 0; q ≥ 2, a global existence and uniqueness theorem is proved. The proof is based on the paper by Long and Truong (Nonlinear Anal. Theory Methods Appl. Ser. A) associated to a contraction mapping theorem and standard arguments of density. In part 2, the asymptotic behavior of the solution u as t → +∞ is studied, under more restrictive conditions, namely g = 0, f(x, t, u) = −|u| p−2 u + F(x, t), p ≥ 2, F ∈ L 1(ℝ+;L 2) ∩ L 2(ℝ+;L 2), , with σ > 0, and (ũ0, ũ1) ∈ H 1 × L 2, k ∈ H 1(ℝ+), and some others (‖ · ‖ denotes the L 2(0,1) norm). It is proved that under these conditions, a unique solution u(t) exists on ℝ+ such that ‖u′(t)‖ + ‖u x (t)‖ decay exponentially to 0 as t → +∞. Finally, we present some numerical results.

Analytic reductions of self-force calculations in curved spacetimes

For the case of an electric or scalar charge travelling along a timelike geodesic in a curved, background spacetime, we apply a Green's theorem argument to transform the tail contribution to the particle's self-force at a point p along its trajectory to a form which involves only an integral over the past light cone from p. One potential advantage of this reformulation is that the tail contribution to the fundamental solution for a (self-adjoint) tensor wave equation in an arbitrary spacetime is (at least within so-called causal domains) explicitly computable on the past light cone of an arbitrary point through the integration of certain linear transport equations defined along the null generators of the cone. The conventional approach to computing the self-force requires this tail field throughout the interior of the past light cone and extracts it from the particle's (numerically generated) total field through an intricate mode-by-mode numerical decomposition. By contrast, our approach requires that the particle's total field be paired with the (explicitly computable) tail field on the light cone itself and then integrated over this cone. We thus avoid the need for the aforementioned mode-by-mode decomposition of the particle's total field into direct ⊕ tail contributions. We speculate that in some circumstances it may be sufficient to truncate the particle's total field, as needed in our calculation, to its (also explicitly computable) direct Liénard Wiechert approximation.

Multiple ionization effects in x-ray emission induced by heavy ions

The x-ray satellite structure of Pd Lalpha1,2(L3M4,5) transition excited by an impact of O7+ and Ne6+ ions with energies 279 and 178 MeV, respectively, which were measured using a high-resolution von Hamos crystal spectrometer, is discussed in terms of the multi-configuration Dirac-Fock (MCDF) calculations. We demonstrate, by using the arguments of the general central limit theorem (GCLT), that a structure of complex M-shell satellites of Pd Lalpha1,2(M-m) transitions for a higher number of spectator vacancies (m > 4), which consists of hundreds of thousands of individual x-ray transitions as obtained from the MCDF calculations, can be well described by a single Voigtian profile. The Lorentzian width of such Voigtian line can be well modeled by using the results of the MCDF calculations for simpler configurations with a number of vacancies m < 4 . This method allows one to describe realistically a complex structure of M-shell satellites, thus extending the applicability of the MCDF calculations, which are limited by an increasing complexity of numerical calculations.

Aharonov-Bohm Superperiod in a Laughlin Quasiparticle Interferometer

We report an Aharonov-Bohm superperiod of five magnetic flux quanta (5h/e) observed in a Laughlin quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. This result does not violate the gauge invariance argument of the Byers-Yang theorem because the magnetic flux, in addition to affecting the Aharonov-Bohm phase of the encircling 1/3 quasiparticles, creates the 2/5 quasiparticles in the island. The superperiod is accordingly understood as imposed by the anyonic statistical interaction of Laughlin quasiparticles.