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We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The algorithm given by this proof seems to be more practical than that given by the original proof. A naive implementation is given at the end of the paper. Another contribution is to show that this result extends to a large class of theories, including simple type theory (higher-order logic) and second-order propositional logic. We obtain this way a new proof of the decidability of the inhabitation problem for positive types in system F.

The self-controlled case series is an important method in the studies of the safety of biopharmaceutical products. It uses the conditional Poisson model to make comparison within persons. In models without adjustment for age (or other time-varying covariates), cases who are never exposed to the product do not contribute any information to the estimation. We provide analytic proof and simulation results that the inclusion of unexposed cases in the conditional Poisson model with age adjustment reduces the asymptotic variance of the estimator of the exposure effect and increases power. We re-analysed a vaccine safety dataset to illustrate. acceptedVersion

We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrodinger equation. This provides an analytic proof of the time period doubling observed in experiments. The experimental check that some pulses generated in optical fibers are indeed such generalized breathers will be drastically simplified.

Sufficient conditions on a smooth, real-valued function g for the nowhere differentiability of $$g\circ p$$ are given, where p is Peano’s curve. This generalizes Sagan’s analytic proof on the nowhere differentiability of the coordinate functions of p. Most of the proofs are geometrically intuitive. The interest about the composites $$g\circ p$$ stems from their recent applications in technical branches.

Influence of component matching errors becomes more and more significant for integrated circuit design, in particular, for digital-to-analog converters. A unary digital-to-analog converter can compensate such errors by means of a switching scheme. This brief proposes a novel technique for a placement of element parts – the Multi-Flip Technique. This technique completely compensates a rotation of an error gradient when using as few as 16 parts for each element. An analytic proof and simulation results confirm its efficiency. Moreover, the technique is capable of being scaled while preserving the property of the rotation compensation.

A resurgence of scholarly work on proof of God’s existence is noticeable over the past decade, with considerable emphasis on attempts to provide ‘analytic proof’ based on the meanings and logic of various identity statements which constitute premises of the syllogisms of the ‘proof’. Most recently perhaps, Emmanuel Rutten’s ‘modal-epistemic proof’ has drawn serious academic attention. Like other ‘analytic’ and strictly logical proofs of God’s existence, Rutten’s proof has been found flawed. In this paper I discuss the possibility of an ‘ethics-based’ identity proof of God’s existence. Such a proof, the first version of which, I believe, has been offered, indirectly, by Nikolai Lossky, utilizes the form and structure of the analytic proof, but fundamentally rests on the perception of moral values we associate with God and Godliness. The nature of the proof shifts the focus of the very attempt to ‘prove’ God’s existence from what I believe is an unreasonable standard, unattainable even in ‘proving’ the existence of the more mundane world, towards a more functional, practical and attainable standard. The proof proposed initially by Lossky, and in a more systematic form here, I believe, shows the indubitable existence of God in the sense of his moral presence in the lives of the faithful, at least with the same degree of certainty as the presence or ‘existence’ of anything else that can be epistemically proven in principle. Tokom poslednje decenije uočljiva je intenziviran rad na izvođenju dokaza o postojanju Boga, sa posebnim naglaskom na takozvane “analitičke dokaze”, koji su zasnovani na značenjima i logici različitih iskaza o identitetu, koji predstavljaju premise samog silogizma “dokaza”. Možda akademski najuticajniji skorašnji analitički dokaz o postojanju Boga izložio je Emanuel Ruten u formi svog “modalno-epistemičkog dokaza”. Kao i za ostale analitčke i strogo logičke dokaze postojanja Boga, i za Rutenov je utvrđeno da je neispravan. Kroz kritiku Rutenovog dokaza, koju koristim kao uvod, ja u ovom tekstu rahzmatram mogućnost dokaza o postojanju Boga koji bi bio zasnovan na etičkim argumentima. Takav dokaz, Like other ‘analytic’ and strictly logical proofs of God’s existence, Rutten’s proof has been found flawed. In this paper I discuss the possibility of an ‘ethics-based’ identity proof of God’s existence. Such a proof, čiju je prvu verziju, po mom mišljenju, već izneo Nikolaj Loski, koristi formu i strukturu analitičkih dokaza, ali se fundamentalno oslanja na doživljaj moralnih vrednosti koje povezujemo sa Bogom ili božanstvenošću. “Etički” dokaz pomera naglasak samog rada na izvođenju dokaza o postojanju Boga sa jednog standarda za koji smatram da je nerazuman i koji se ne može dostići ni kada se “dokazuje” postojanje mnogo manje kontroverznih ontoloških kategorija, kao što su različite kategorije svakodnevnog, “običnog” sveta. Istovremeno, etički dokaz pomera naglasak dokazivanja ka jednom funkcionalnom, praktičnom i dostižnom standardu dokazivanja. Ovaj dokaz, i u formi u kojoj ga je izveo Loski, a i u sistematičnijoj formi u kojoj ga ovde izlažem, pokazuje nesumnjivo postojanje Boga u smislu moralnog prisustva Boga u životima verujućih ljudi. “Izvesnost” takvog dokaza nije ništa manja od izvesnosti bilo čega drugog što se uopšte može epistemički dokazivati.

For models describing water waves, Constantin and Escher's works have long been considered as the cornerstone method for proving wave breaking phenomena. Their rigorous analytic proof shows that if the lowest slope of flows can be controlled by its highest slope initially, then the wave-breaking occur for the Whitham-type equation. Since this breakthrough, there have been numerous refined wave-breaking results established by generalizing the kernel which describes the dispersion relation of water waves. Even though the proofs of these involve a system of coupled Riccati-type differential inequalities, however, little or no attention has been made to a generalization of this Riccati-type system. In this work, from a rich class of non-local conservation laws, a Riccati-type system that governs the flow's gradient is extracted and investigated. The system's leading coefficient functions are allowed to change their values and signs over time as opposed to the ones in many of other previous works are fixed constants. Up to the author's knowledge, the blow-up analysis upon this structural generalization is new and is of theoretical interest in itself as well as its application to various non-local flow models. The theory is illustrated via the Whitham-type equation with nonlinear drift. Our method is applicable to a large class of non-local conservation laws.

We compute the diagonal restriction of the first derivative with respect to the weight of a p-adic family of Hilbert modular Eisenstein series attached to a general (odd) character of the narrow class group of a real quadratic field, and express the Fourier coefficients of its ordinary projection in terms of the values of a distinguished rigid analytic cocycle in the sense of Darmon and Vonk (Duke Math J, to appear, 2020) at appropriate real quadratic points of Drinfeld’s p-adic upper half-plane. This can be viewed as the p-adic counterpart of a seminal calculation of Gross and Zagier (J Reine Angew Math 355:191–220, 1985, §7) which arose in their “analytic proof” of the factorisation of differences of singular moduli, and whose inspiration can be traced to Siegel’s proof of the rationality of the values at negative integers of the Dedekind zeta function of a totally real field. Our main identity enriches the dictionary between the classical theory of complex multiplication and its extension to real quadratic fields based on RM values of rigid meromorphic cocycles, and leads to an expression for the p-adic logarithms of Gross–Stark units and Stark–Heegner points in terms of the first derivatives of certain twisted Rankin triple product p-adic L-functions.

The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic.

Proving or disproving an information inequality is a crucial step in establishing the converse results in coding theorems. However, an information inequality involving more than a few random variables is difficult to be proved or disproved manually. In 1997, Yeung developed a framework that uses linear programming for verifying linear information inequalities. Under the framework, this paper considers a few other problems that can be solved by using Lagrange duality and convex approximation. We will demonstrate how linear programming can be used to find an analytic proof of an information inequality or an analytic counterexample to disprove it if the inequality is not true in general. The way to automatically find a shortest proof or a smallest counterexample is explored. When a given information inequality cannot be proved, the sufficient conditions for a counterexample to disprove the information inequality are found by linear programming. Lastly, we propose a scalable algorithmic framework based on the alternating direction method of multipliers to accelerate solving a multitude of user-specific problems whose overall computational cost can be amortized with the number of users, and present its publicly-available software implementation for large-scale problems.

We give a direct analytic proof of the classical Boundary Harnack Principle for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.

We derive the Simon–Wolff localization criterion from the spectral averaging using an intuitive measure-theoretic lemma.

We aim to raise awareness of the omitted variable bias (i.e., one special form of endogeneity) and highlight its severity for causal claims. Firstly, we demonstrate via analytic proof that omitting a relevant variable from a model which explains the independent and dependent variable leads to biased estimates. Secondly, we offer an easy-to-understand visualization for the problem. Finally, we discuss two remedies, diminishing the risk of the omitted variable bias, namely the instrument variable or two-stage least squares estimator and the regression discontinuity design. We hope that our review will motivate researchers to use them more often in future research.

[EN] There are recent results concerning the boundedness and also unboundedness of Bergman projections on weighted spaces of the unit disc in special cases of rapidly decreasing weights, i.e. "large" Bergman spaces. The aim of our paper is to show that the cases of boundedness are largely exceptional: in general the Bergman projections are unbounded. In addition we give a new, more functional analytic proof for the known central boundedness case which also enables us to transfer our results to harmonic Bergman spaces., The research of Bonet was partially supported by the project MCIN PID2020-119457GB-I00/AEI/10.13039/501100011033. The research of Taskinen was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.

Quantum teleportation (QT) lies at the heart of modern day quantum information science and technology. Despite extensive studies over past two decades, obtaining the necessary and/or sufficient criterion for QT with continuous-variable (CV) resources, besides entanglement, still remains an open concern. In this backdrop, here we analyze the role of a purely quantum optical (QO) attribute, known as quadrature squeezing, in CV teleportation. We first provide an analytic proof that for Gaussian resources quadrature squeezing is necessary for QT. However, for non-Gaussian resources we show a clear distinction between the pure and the mix states. For the pure states, quadrature squeezing appears to be necessary for QT, in the sense that there is no QT without quadrature squeezing. However, in the case of mix states we observe otherwise, i.e., QT could be achieved even without quadrature squeezing. Our results present the exotic character of the QO attributes of the CV resources and necessitate a deeper search for the necessary and/or sufficient criterion for CV QT.

The basic aim of this paper is to provide a fundamental tool, the resolvent decomposition theorem, in the construction theory of denumerable Markov processes. We present a detailed analytic proof of this extremely useful tool and explain its clear probabilistic interpretation. We then apply this tool to investigate the basic problems of existence and uniqueness criteria for denumerable Markov processes with instantaneous states to which few results have been obtained even until now. Although the complete answers regarding these existence and uniqueness criteria will be given in a subsequent paper, we shall, in this paper, present part solutions of these very important problems that are closely linked with the subtle Williams S and N conditions.

We study the class P of positive linear functionals φ on L ∞ ( [ 1 , ∞ ) ) for which φ ( f ) = α if lim x → ∞ 1 x ∫ 1 x f ( t ) d t = α . The semigroup of translations f ( x ) ↦ f ( r x ) on L ∞ ( [ 1 , ∞ ) ) , where r ∈ [ 1 , ∞ ) , plays a crucial role in the study of P . In particular, we give three different expressions of their extremal values, which can be considered main results of this paper. We also study linear functionals on l ∞ , the set of all real-valued bounded functions on natural numbers N , which extend Cesaro mean and give similar results about their extremal values, including a functional analytic proof of the classical result of Polya.

Given two ideals $\mathcal{I}$ and $\mathcal{J}$ of holomorphic functions such that $\mathcal{I} \subseteq \mathcal{J}$, we describe a comparison formula relating the Andersson-Wulcan currents of $\mathcal{I}$ and $\mathcal{J}$. More generally, this comparison formula holds for residue currents associated to two generically exact Hermitian complexes together with a morphism between the complexes. One application of the comparison formula is a generalization of the transformation law for Coleff-Herrera products to Andersson-Wulcan currents of Cohen-Macaulay ideals. We also use it to give an analytic proof by means of residue currents of theorems of Hickel, Vasconcelos and Wiebe related to the Jacobian ideal of a holomorphic mapping., Comment: 22 pages, v6: Minor sign correction in equation (3.4)

Bu araştırmada ilköğretim matematik öğretmeni adaylarının öğrenme stillerinin ve trigonometri konusunda tercih ettikleri kanıt şemalarının belirlenmesi ve bunların farklı değişkenler açısından incelenerek kanıt şemalarının öğrenme stillerine göre değişimini ortaya koymak amaçlanmıştır. Bu amaç doğrultusunda tarama yönteminin kullanıldığı bu araştırmada 2013-2014 eğitim öğretim yılında Kastamonu Üniversitesi Eğitim Fakültesi İlköğretim Bölümü Matematik Öğretmenliği Anabilim Dalında öğrenim gören 170 öğretmen adayı araştırmanın çalışma grubunu oluşturmuştur. Araştırmada veri toplama aracı olarak Kolb öğrenme stili envanteri ve Trigonometri İspat Envanteri (TİE) kullanılmıştır. Katılımcıların öğrenme stilleri, envantere verilen yanıtlara göre belirlenirken, kanıt şemaları betimsel analiz yöntemi ile belirlenmiştir. Araştırmadan elde edilen bulgulara göre katılımcılar arasında baskın olan öğrenme stilinin özümseyen olduğu ve aynı zamanda öğrenme stillerinin cinsiyete ve sınıf düzeyine göre farklılaşmadığı görülmüştür. Bununla birlikte katılımcıların en çok analitik kanıt şemasını kullanmayı tercih ettiği ve kanıt yaparken kullandıkları kanıt şemalarının öğrenme stillerine göre farklılaşmadığı tespit edilmiştir.

In this paper, we study transcendental aspects of the cohomology groups of adjoint bundles of log canonical pairs, aiming to establish an analytic theory for log canonical singularities. As a result, in the case of purely log terminal pairs, we give an analytic proof of the injectivity theorem originally proved by the Hodge theory. Our method is based on the theory of harmonic integrals and the L2-method for the dbar-equation, and it enables us to generalize the injectivity theorem to the complex analytic setting., Comment: 26pages, comments welcome

G~, the extension of Godel logic $G$ with an invo-lutive negation, has many applications, like its use as a fuzzy paraconsistent logic. In this paper we provide analytic proof systems for both the truth-preserving and the degree-preserving versions of G~, as well as to its proper extensions in its language. In addition, we provide particularly simple Hilbert-type axiomatizations of these logics, which (unlike previous such axiomatizations) do not use Baaz’ Δ operator. Instead, we follow a suggestion made (and left open) in [16], and base our systems on using, in addition to (MP), the rule (CP). (from φ → ψ infer ⇁ψ → ⇁φ). This establishes an interesting connection between G~, and some major modal logics (like $B$ and $S$ 5).

“\(V-E+F=2\)”, the famous Euler’s polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as the Euler–Poincare Formula. We provide another short inductive combinatorial proof of the general formula. Our proof is self-contained and it does not use shellability of polytopes.

Agraïments: The second author is partially supported by NNSF of China grant 10671123 and NCET of China grant 050391. He thanks the Centre de Recerca Matemàtica for the hospitality and the financial support by the grant SAB2006-0098 (Ministerio de Educación y Ciencia, Spain). Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof on the existence of a Hopf-zero bifurcation for the Michelson system x2 x˙ = y, y˙ = z, z˙ = c2 − y − , 2 at c = 0. Moreover our method estimates the shape of this periodic orbit in function of c > 0 sufficiently small.

A rigorous proof for the existence of the second law of thermodynamics added as an appendix because of the distracting complexity of the mathematical developments. Again, this is not usually included in standard monographs.

In this article, we propose the Abbas-Nazir three step iteration scheme and employ the algorithm to study the common fixed points of a pair of generalized $\alpha$-Reich-Suzuki non-expansive mappings defined on a Banach space. Moreover, we explore a few weak and strong convergence results concerning such mappings. Our findings are aptly validated by non-trivial and constructive numerical examples and finally, we compare our results with that of the other noteworthy iterative schemes utilizing MATLAB $2017$a software. However, we perceive that for a different set of parameters and initial points, the newly proposed iterative scheme converges faster than the other well-known algorithms. To be specific, we give an analytic proof of the claim that the novel iteration scheme is also faster than that of Liu et al.

This is the second part of a survey on the theory of non-Archimedean curves and Schottky uniformization from the point of view of Berkovich geometry. It is more advanced than the first part and covers the theory of Mumford curves and Schottky uniformization. We start by briefly reviewing the theory of Berkovich curves, then introduce Mumford curves in a purely analytic way (without using formal geometry). We define Schottky groups acting on the Berkovich projective line, highlighting how geometry and group theory come together to prove that the quotient by the action of a Schottky group is an analytic Mumford curve. Finally, we present an analytic proof of Schottky uniformization, showing that any analytic Mumford curve can be described as a quotient of this kind. The guiding principle of our exposition is to stress notions and fully prove results in the theory of non-Archimedean curves that, to our knowledge, are not fully treated in other texts.

The aim of this paper is to study the more accurate existence results of positive solution for a nonlinear fourth order ordinary differential equation (for short NLFOODE) using four-point boundary value conditions (for short BVCs). The upper and lower solution method and Schauder’s fixed point theorem have been applied to demonstrate the obtained existence results. First, the Green’s function of the corresponding linear boundary value problem (for short BVP) has been constructed and then it is used to solve the considered BVP of this paper. An example has also been included at the end of this paper to support the analytic proof.

Critical transition points between symmetry-broken phases are usually characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that iteratively traces out the large-momentum modes, this well-known fact can easily break down in non-Hermitian systems under open boundary conditions. Based on non-Hermitian Su-Schrieffer-Heeger-type models, we propose a RG scheme based on real-space decimation. We provide concrete examples and an analytic proof to show that the real-space scheme always respects the critical points under RG transformations. We investigate the correlation length of order parameters in the vicinity of critical points. Its divergence and scaling behavior remain intact under the real-space decimation, indicating that our method can be successfully applied to study the critical phenomena in non-Hermitian systems. These results suggest that the real-space RG method will find versatile applications in interacting non-Hermitian quantum systems.

Euler used his product expansion of the Riemann zeta function $$ \zeta (s)\ =\ \sum ^\infty _{n=1}\frac{1}{n^s}\ =\ \prod _{p\ \mathrm{prime}} \left( 1-\frac{1}{p^s}\right) ^{-1},\qquad \mathrm{Re\,}s>1 $$ to give an analytic proof that there are infinitely many primes.

In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then follows by induction. This solves a problem posed by R. Stanley in 2008. Our proof is based on Andersons analytic proof of the formula. As part of the proof we show a further generalisation of the generalised Vandermonde determinant.

We use that the n-sphere for \(n\ge 2\) is simply-connected to prove the Poincare-Birkhoff-Witt Theorem.

We propose a novel complex-analytic method for sums of i.i.d. random variables that are heavy-tailed and integer-valued. The method combines singularity analysis, Lindel\"of integrals, and bivariate saddle points. As an application, we prove three theorems on precise large and moderate deviations which provide a local variant of a result by S. V. Nagaev (1973). The theorems generalize five theorems by A. V. Nagaev (1968) on stretched exponential laws $p(k) = c\exp( -k^\alpha)$ and apply to logarithmic hazard functions $c\exp( - (\log k)^\beta)$, $\beta>2$; they cover the big jump domain as well as the small steps domain. The analytic proof is complemented by clear probabilistic heuristics. Critical sequences are determined with a non-convex variational problem., Comment: 32 pages, 3 figures

© 2017, Springer Science+Business Media B.V. In this paper we give a new proof of the Nešetřil–Rödl Theorem, a deep result of discrete mathematics which is one of the cornerstones of the structural Ramsey theory. In contrast to the well-known proofs which employ intricate combinatorial strategies, this proof is spelled out in the language of category theory and the main result follows by applying several simple categorical constructions. The gain from the approach we present here is that, instead of giving the proof in the form of a large combinatorial construction, we can start from a few building blocks and then combine them into the final proof using general principles.

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is apparent. Secondly we give an analytic proof of the duality from the viewpoint of our previous study of zeta-functions of Arakawa-Kaneko type. As an application, we give a formula that relates poly-Bernoulli numbers to the Genocchi numbers., 14 pages

Consider a K-uniform hypergraph H = (V, E). A coloring c: V → {1, 2, …, k} with k colors is rainbow if every hyperedge e contains at least one vertex from each color, and is called perfectly balanced when each color appears the same number of times. A simple polynomial-time algorithmnds a 2-coloring if H admits a perfectly balanced rainbow k-coloring. For a hypergraph that admits an almost balanced rainbow coloring, we prove that it is NP-hard to find an independent set of size ϵ, for any ϵ > 0. Consequently, we cannot weakly color (avoiding monochromatic hyperedges) it with O(1) colors. With k=2, it implies strong hardness for discrepancy minimization of systems of bounded set-size. One of our main technical tools is based on reverse hypercontractivity. Roughly, it says the noise operator increases q-norm of a function when q < 1, which is enough for some special cases of our results. To prove the full results, we generalize the reverse hypercontractivity to more general operators, which might be of independent interest. Together with the generalized reverse hypercontractivity and recent developments in inapproximability based on invariance principles for correlated spaces, we give a recipe for converting a promising test distribution and a suitable choice of an outer PCP to hardness of nding an independent set in the presence of highly-structured colorings. We use this recipe to prove additional results almost in a black-box manner, including: (1) the rst analytic proof of (K − 1 − ϵ)-hardness of K-Hypergraph Vertex Cover with more structure in completeness, and (2) hardness of (2Q+1)-SAT when the input clause is promised to have an assignment where every clause has at least Q true literals.

In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic logic 2Int. The proof makes use of the faithful embedding of 2Int into intuitionistic logic with respect to validity and shows that conversions of dual proofs can be sidestepped.