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Build systems are awesome, terrifying – and unloved. They are used by every developer around the world, but are rarely the object of study. In this paper, we offer a systematic, and executable, framework for developing and comparing build systems, viewing them as related points in a landscape rather than as isolated phenomena. By teasing apart existing build systems, we can recombine their components, allowing us to prototype new build systems with desired properties. [ABSTRACT FROM AUTHOR]

In this paper we discuss the concept of a Z-sequence and use it to define the Fibonacci Z-sequence. Based on Z-sequences one may define analogs of logarithm functions. The special case of the logarithm function associated with the Fibonacci Z-sequence is of interest, since the recursive property of this sequence permits a more detailed study of these functions. They are similar to ordinary logarithm functions which may be based onZ-sequences {an}nϵZ, where a > 1. [ABSTRACT FROM AUTHOR]

Shuford, Albert, and Massengill proved, a half century ago, that the logarithmic scoring rule is the only proper measure of inaccuracy determined by a differentiable function of probability assigned the actual cell of a scored partition. In spite of this, the log rule has gained less traction in applied disciplines and among formal epistemologists that one might expect. In this article we show that the differentiability criterion in the Shuford et al. result is unnecessary and use the resulting simplified characterization of the logarithmic rule to give novel arguments in favor of it. [ABSTRACT FROM AUTHOR]

We show that even mild improvements of the Pólya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of the second author jointly with J. Bober and Y. Lamzouri) and a quantitative relationship between the mean and the logarithmic mean of a completely multiplicative function. [ABSTRACT FROM AUTHOR]

In this paper we discuss some convergence and divergence properties of subsequences of logarithmic means of Walsh-Fourier series. We give necessary and sufficient conditions for the convergence regarding logarithmic variation of numbers. [ABSTRACT FROM AUTHOR]

We prove the Valiron-type and Valiron-Titchmarsh-type theorems for entire functions of order zero with zeros on a logarithmic spiral. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of lower Q-homeomorphisms relative to a p-modulus in ℝn, n ≥ 2, at a point is studied. A number of logarithmic estimates for the lower limits under various conditions imposed on the function Q are obtained. Some applications of these results to the Orlicz-Sobolev classes Wloc1,φ in ℝn, n ≥ 3 under the Calderon-type condition imposed on the function φ and, in particular, to the Sobolev classes Wloc1,p for p > n - 1 are given. The example of a homeomorphism with finite distortion which shows the exactness of the found order of growth is constructed. [ABSTRACT FROM AUTHOR]

We consider a general two-component plasma of classical pointlike charges +e (e is say the elementary charge) and -Ze (valency Z=1,2,…), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature β, in the stability region against collapse of oppositely charged particle pairs βe2<2/Z. We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential βΩ. By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any βe2<2/Z the large-R expansion of the grand potential is of the form βΩ∼AVR2+χ/6-β(Qe)2/2lnR, where AV is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere χ=2. The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (χ=1), in the case of the symmetric (Z=1) two-component plasma at the collapse point βe2=2 and the jellium model (Z→0) of identical e-charges in a fixed neutralizing background charge density at any coupling βe2 being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part -β(Qe)2/2 is independent of the geometry of the confining domain. [ABSTRACT FROM AUTHOR]

Abstract: The first part of the paper studies the expression for, and the properties of, the logarithm map on an orthant space, which is a simple stratified space, with the aim of analysing Fréchet means of probability measures on such a space. In the second part, we use these results to characterise Fréchet means and to derive various of their properties, including the limiting distribution of sample Fréchet means. [ABSTRACT FROM AUTHOR]

In this paper, we present a general comparison theorem for two divided differences of a three times differentiable function. This gives a unified treatment for (logarithmically) complete monotonicity, monotonicity and inequalities involving some special functions including gamma, psi and polygamma functions. As their consequences, we not only refine and generalize some important results, but also present simple and interesting alternative proofs of certain earlier results. [ABSTRACT FROM AUTHOR]

In this paper, some Ostrowski's inequalities for functions whose first derivatives are s-logarithmically preinvex in the second sense are established. [ABSTRACT FROM AUTHOR]

We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schrödinger operator, as well as for operators with compactly supported time-independent potentials, a sharp analog of the Hardy uncertainty principle is obtained, using an argument based on the theory of entire functions. Logarithmic convexity of weighted norms is employed in the case of general bounded potentials. [ABSTRACT FROM AUTHOR]

We shall establish some criteria on entire series with finite logarithmic order in terms of maximum term and central index. [ABSTRACT FROM AUTHOR]

We consider the porous medium equation in an exterior two-dimensional domain that excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in 2007 that in the far-field scale, which is the adequate one to describe the movement of the free boundary, solutions to this problem with integrable and compactly supported initial data behave as an instantaneous point-source solution for the equation with a variable mass that decays to 0 in a precise way, determined by the initial data and the hole. In this paper, starting from their result in the far field, we study the large time behavior in the near field, in scales that evolve more slowly than the free boundary. In this way we get, in particular, the final profile and decay rate on compact sets. Spatial dimension two is critical for this problem, and involves logarithmic corrections. [ABSTRACT FROM AUTHOR]

In this study, a method for the analytical evaluation of globally optimal solutions for the minimum weight design of trusses is presented. The basis of the methodology is the cylindrical algebraic decomposition algorithm, in tandem with powerful symbolic computation for the discovery of stationary points. Certain final answers to well-known benchmark problems are produced, while future improvements in both the algorithm implementation and the computer capabilities may allow the solution of even more difficult problems. To the best of our knowledge, no similar attempt can be found in the literature. [ABSTRACT FROM AUTHOR]

The zeros of the digamma function are known to be simple and real, but up to now few identities involving them have appeared in the literature. By establishing a Weierstrass infinite product for a particular regularization of the digamma function, we are able to find interesting formulas for the sums of thenth powers of the reciprocals of its zeros, for. We make a parallel study of the zeros of the logarithmic derivative of the BarnesG-function. We also compare asymptotic estimates of the zeros of the digamma function and those of its BarnesG-function analogue. [ABSTRACT FROM PUBLISHER]

The so-called Schwab-Borchardt mean plays an important role in the theory of (bivariate) means. It includes a lot of standard means, such as the logarithmic mean, the first and second Seiffert means and the Neuman-Sándor mean. In this paper, we investigate an approach which allows us to construct a class of new means. Such class includes the (generalized) Schwab-Borchardt mean and other old/new means derived as well. [ABSTRACT FROM AUTHOR]

In this paper, we find the greatest values $\alpha_{1},\alpha_{2}$ and the smallest values $\beta_{1},\beta_{2}$ such that the double inequalities $L_{\alpha_{1}}(a,b)<\operatorname{AG}(a,b)0$ with $a\neq b$ , where $\operatorname{AG}(a,b)$ , $T(a,b)$ and $L_{p}(a,b)$ are the arithmetic-geometric, Toader and generalized logarithmic means of two positive numbers a and b, respectively. [ABSTRACT FROM AUTHOR]

We provide a new characterization of the logarithmic Sobolev inequality. [ABSTRACT FROM AUTHOR]

We study actions of diagonalizable groups on toroidal schemes (i.e. logarithmically regular logarithmic schemes). In particular, we show that for so-called toroidal actions the quotient is again a toroidal scheme. Our main result constructs for an arbitrary action a canonical torification by an equivariant blowings up. This extends earlier results of Abramovich–de Jong, Abramovich–Karu–Matsuki–Włodarczyk, and Gabber in various aspects. [ABSTRACT FROM AUTHOR]

Aproblem of a straight mixed mode non-interface fracture in an infinite plane is treated analytically with the help of complex analysis techniques. The surfaces of the fracture are subjected to surface elasticity in the form proposed by Steigmann and Ogden (Steigmann and Ogden, Proc. R. Soc. A 453 (1997); Steigmann and Ogden, Proc. R. Soc. A 455 (1999)). The boundary conditions on the banks of the fracture connect the stresses and the derivatives of the displacements. The mechanical problem is reduced to two systems of singular integro-differential equations which are further reduced to the systems of equations with logarithmic singularities. It is shown that modeling of the fracture with the Steigmann-Ogden elasticity produces the stress and strain fields, which are bounded at the crack tips. The existence and uniqueness of the solution for almost all the values of the parameters is proved. Additionally, it is shown that introduction of the surface mechanics into the modeling of fracture leads to the size-dependent equations. A numerical scheme of the solution of the systems of singular integro-differential equations is suggested, and the numerical results are presented for different values of the mechanical and the geometric parameters. [ABSTRACT FROM AUTHOR]

Let P be an m -homogeneous polynomial in n -complex variables x 1 , … , x n . Clearly, P has a unique representation in the form P ( x ) = ∑ 1 ≤ j 1 ≤ … ≤ j m ≤ n c ( j 1 , … , j m ) x j 1 ⋯ x j m , and the m -form L P ( x ( 1 ) , … , x ( m ) ) = ∑ 1 ≤ j 1 ≤ … ≤ j m ≤ n c ( j 1 , … , j m ) x j 1 ( 1 ) ⋯ x j m ( m ) satisfies L P ( x , … , x ) = P ( x ) for every x ∈ C n . We show that, although L P in general is non-symmetric, for a large class of reasonable norms ‖ ⋅ ‖ on C n the norm of L P on ( C n , ‖ ⋅ ‖ ) m up to a logarithmic term ( c log ⁡ n ) m 2 can be estimated by the norm of P on ( C n , ‖ ⋅ ‖ ) ; here c ≥ 1 denotes a universal constant. Moreover, for the ℓ p -norms ‖ ⋅ ‖ p , 1 ≤ p < 2 the logarithmic term in the number n of variables is even superfluous. [ABSTRACT FROM AUTHOR]

A fractionally integrated inverse stable subordinator (FIISS) is the convolution of an inverse stable subordinator, also known as a Mittag-Leffler process, and a power function. We show that the FIISS is a scaling limit in the Skorokhod space of a renewal shot noise process with heavy-tailed, infinite mean ‘inter-shot’ distribution and regularly varying response function. We prove local Hölder continuity of FIISS and a law of iterated logarithm for both small and large times. [ABSTRACT FROM AUTHOR]

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilization and control. [ABSTRACT FROM AUTHOR]

Given an input x and a search problem F , local computation algorithms (LCAs) implement access to specified locations of y in a legal output y ∈ F ( x ) , using polylogarithmic time and space. Parnas and Ron [27] and Mansour et al. [19] showed how to convert certain distributed and online algorithms to LCAs, respectively. In this work, we expand on those lines of work and develop new techniques for designing LCAs and bounding their space and time complexity. [ABSTRACT FROM AUTHOR]

The article focuses on a study conducted to analyze the sharp bounds for the problem of Steklov. The logarithmic factor in the denominator is not determined. A version of Steklov problem is used to obtain the bounds on the sequence of polynomials. One of the most basic and most well-studied problems in approximation theory is explained.

We select subclasses of zero-order entire functions f for which we present sufficient conditions for the existence of the $$ \upsilon $$ -density of zeros of f in terms of the asymptotic behavior of the logarithmic derivative F and regular growth of the Fourier coefficients of F. [ABSTRACT FROM AUTHOR]

Inspired by a description of the logarithmic space of Kato and Nakayama in terms of real oriented blowups, we describe Milnor fibrations and related constructions used by A'Campo in the language of logarithmic geometry. [ABSTRACT FROM AUTHOR]

The goal of this paper is to generalize and refine the classical ramification theory of complete discrete valuation rings to more general valuation rings, in the case of Artin–Schreier extensions. We define refined versions of invariants of ramification in the classical ramification theory and compare them. Furthermore, we can treat the defect case. [ABSTRACT FROM AUTHOR]

We study the large time behavior of nonnegative solutions to the Cauchy problem for a fast diffusion equation with critical zero order absorption ∂ t u − Δ u m + u q = 0 in ( 0 , ∞ ) × R N , with m c : = ( N − 2 ) + / N < m < 1 and q = m + 2 / N . Given an initial condition u 0 decaying arbitrarily fast at infinity, we show that the asymptotic behavior of the corresponding solution u is given by a Barenblatt profile with a logarithmic scaling, thereby extending a previous result requiring a specific algebraic lower bound on u 0 . A by-product of our analysis is the derivation of sharp gradient estimates and a universal lower bound, which have their own interest and hold true for general exponents q > 1 . [ABSTRACT FROM AUTHOR]

An asymptotic limit of a class of Cahn–Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose–Fife type, fast diffusion equation and so on. Namely, by setting the suitable potential of the Cahn–Hilliard systems, all these problems can be obtained as limits of the Cahn–Hilliard related problems. Convergence results and error estimates are proved. [ABSTRACT FROM AUTHOR]

In this paper we consider the additive logarithmic finite strain plasticity formulation from the view point of loss of ellipticity in elastic unloading. We prove that even if an elastic energy F ↦ W ( F ) = W ^ ( log U ) defined in terms of logarithmic strain log U , where U = F T F , happens to be everywhere rank-one convex as a function of F , the new function F ↦ W ˜ ( F ) = W ^ ( log U − log U p ) need not remain rank-one convex at some given plastic stretch U p (viz. E p log ≔ log U p ). This is in complete contrast to multiplicative plasticity (and infinitesimal plasticity) in which F ↦ W ( F F p − 1 ) remains rank-one convex at every plastic distortion F p if F ↦ W ( F ) is rank-one convex ( ∇ u ↦ ∥ sym ∇ u − ε p ∥ 2 remains convex). We show this disturbing feature of the additive logarithmic plasticity model with the help of a recently introduced family of exponentiated Hencky energies. [ABSTRACT FROM AUTHOR]

We show that the Szász-Mirakyan and Baskakov operators preserve the logarithmic convexity of functions, whereas the Bernstein and Kantorovich operators do not possess this property. [ABSTRACT FROM AUTHOR]

The article reports on the significance of logarithmic scales. The principle of estimation is built into logarithmic scales and logarithmic scales give the geometric mean an intuitive interpretation. The geometric mean of two quantities a and b is simply their midpoint if they are placed on a logarithmic scale.

In his lost notebook, Ramanujan recorded two identities involving double series of Bessel functions that are closely connected with the classical, unsolved circle and divisor problems. In a series of papers with Zaharescu, the authors proved these identities under various interpretations, as well as Riesz mean analogues. In this paper, logarithmic mean analogues, also involving double series of Bessel functions, are established. Weighted divisor sums involving characters play a central role. [ABSTRACT FROM AUTHOR]

We compute the $p$-adic $L$-functions of evil Eisenstein series, showing that they factor as products of two Kubota–Leopoldt $p$-adic $L$-functions times a logarithmic term. This proves in particular a conjecture of Glenn Stevens. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the regularity criterion of the weak solutions of the two-dimensional supercritical surface quasi-geostrophic equation in a critical Morrey space. It is proved that if the weak solution θ ( x , t ) of the supercritical quasi-geostrophic equation satisfies the growth condition ∫ 0 T ‖ ∇ θ ( t ) ‖ M ̇ p , q r 1 + ln ( e + ‖ ∇ θ ‖ L p ) d t < ∞ with 2 p + α r = α , 2 α < p < ∞ , then the solution θ ( x , t ) is regular on R 2 × ( 0 , T ] . This improves the earlier results by Xiang (2010). [ABSTRACT FROM AUTHOR]

In this paper, a novel L ∞ analysis for finite volume approximations of the Stokes problem is presented. Optimal order estimates in the L ∞ -norm for the velocity gradient and pressure of this problem are obtained by using new technical results. In particular, these optimal error estimates for the finite volume approximations are obtained without the presence of a usual logarithmic factor O ( | log h | ) for the stationary Stokes problem. Several numerical tests are performed to check these theoretical expectations. [ABSTRACT FROM AUTHOR]

Under mild conditions, we find the best linear prediction of linear processes with arbitrary innovations. The prediction method is based on the theory of Hilbert spaces. Using the presented method we can predict non-causal ARMA processes. Finally, we utilize the presented method for prediction of natural logarithms of volumes of Wal-Mart stock traded daily. [ABSTRACT FROM AUTHOR]

We study the distribution of values of the solutions of an algebraic differential equation P( z, f, f′, . . . , f) = 0 with the property that its coefficients and solutions have a branching point at infinity (e.g., a logarithmic singularity). It is proved that if a ∈ ℂ is a deficiency value of f and f grows faster than the coefficients, then the following identity takes place: P( z, a, 0 , . . . , 0) ≡ 0 , z ∈ { z : r ≤ |z| < ∞} . If P( z, a, 0 , . . . , 0) is not identically equal to zero in the collection of variables z and a, then only finitely many values of a can be deficiency values for the solutions f ∈ M with finite order of growth. [ABSTRACT FROM AUTHOR]

The equilibrium measure, μ , associated with an external field, φ , defined on Σ ⊂ R and such that there exists a point x 0 and an open interval, I , with x 0 ∈ I ⊂ Σ , φ being continuous in I but analytic in I ∖ { x 0 } , is studied. It is shown that the main asymptotic term of the derivatives of φ at both sides of x 0 determines the local behavior of Supp ( μ ) and the local behavior of the density associated with μ . Some results related to a “forbidden region” for Supp ( μ ) are obtained. Also the behavior of the density associated with μ is obtained when x 0 is contained in the interior of the support. [ABSTRACT FROM AUTHOR]

This paper is concerned with the parabolic-elliptic Keller-Segel system with singular sensitivity and logistic source, { u t = Δ u − χ ∇ ⋅ ( u v ∇ v) + r u − μ u 2, x ∈ Ω, t > 0, 0 = Δ v − v + u, x ∈ Ω, t > 0, under homogeneous Neumann boundary conditions in a smoothly bounded domain Ω ⊂ R 2, where χ > 0, r ∈ R, μ > 0, with nonnegative initial data 0 ≢ u 0 ∈ C 0 ( Ω ̄ ) . It is shown that in this two-dimensional setting, the absorptive character of the logistic kinetics is sufficient to enforce global existence of classical solutions even for arbitrarily large χ > 0 and any μ > 0 and r ∈ R . It is moreover shown that if in addition r > 0 is sufficiently large then all these solutions are uniformly bounded. A main step in the derivation of these results consists of establishing appropriate positive a priori bounds from below for the mass functional ∫ Ω u, which due to the presence of logistic kinetics is not preserved. These in turn provide pointwise lower bounds for v, which then allow for the choice of p > 1, explicitly depending inter alia on inf v, such that ∫ Ω u p (x, t) d x can be suitably bounded from above. [ABSTRACT FROM AUTHOR]