Turbulence Phenomena in Real Analysis

Logical approaches-and ontologies in particular-offer a well-adapted framework for representing knowledge present on the Semantic Web ( Open image in new window ). These ontologies are formulated in Open image in new window ( Open image in new window ), which are based on expressive Open image in new window ( Open image in new window ). Open image in new window are a subset of Open image in new window ( Open image in new window ) that provides decidable reasoning. Based on Open image in new window , it is possible to rely on inference mechanisms to obtain new knowledge from axioms, rules and facts specified in the ontologies. However, these classical inference mechanisms do not deal with : Open image in new window probabilities. Several works recently targeted those issues (i.e. Open image in new window , Open image in new window , Open image in new window , etc.), but none of them combines Open image in new window with Open image in new window ( Open image in new window ) formalism. Several open source software packages for Open image in new window are available (e.g. Open image in new window , Open image in new window , Open image in new window , etc.). In this paper, we present Open image in new window , a Java framework for reasoning with probabilistic information in the Open image in new window . Open image in new window incorporate three open source software packages for Open image in new window , which is able to reason with uncertainty information, showing that it can be used in several real-world domains. We also show several experiments of our tool with different ontologies.

Let {\mathcal L}^p_{\alpha}(U^n) denote the class of all measurable functions defined on the unit polydisc U^n=\{z\in {\bf C}^n\, \big| \;|z_i|<1,\ i=1,...,n\} such that \|f\|^p_{{\mathcal L}_{\alpha}(U^n)}=\int_{U^n}|f(z)|^p\prod_{j=1}^n (1-|z_j|^2)^{\alpha_j}dm(z_j)<\infty, where \alpha_j>-1 , j=1,...,n , and dm(z_j) is the normalized area measure on the unit disk U , H(U^n) the class of all holomorphic functions on U^n , and let {\mathcal A}^p_{\alpha}(U^n)={\mathcal L}^p_{\alpha}(U^n) \cap H(U^n) (the weighted Bergman space). In this paper we prove that for p\in (0,\infty), f\in {\mathcal A}^p_{\alpha}(U^n) if and only if the functions \prod_{j\in S}(1-|z_j|^2)\frac{\partial ^{|S|} f} {\prod_{j\in S}\partial z_j}\big(\chi_S(1)z_1, \chi_S(2)z_2,..., \chi_S(n)z_n\big) belong to the space {\cal L}^p_{\alpha}(U^n) for every S\subseteq \{1,2,...,n\}, where \chi_S(\cdot) is the characteristic function of S, |S| is the cardinal number of S, and \prod_{j\in S}\partial z_j=\partial z_{j_1}\cdots\partial z_{j_{|S|}}, where j_k\in S, \, k=1,...,|S|. This result extends Theorem 22 of Kehe Zhu in Trans. Amer. Math. Soc. 309 (1988) (1), 253–268, when p\in (0,1). Also in the case p\in [1,\infty) , we present a new proof.

We investigate experimentally the effect of aspect ratio ( Open image in new window ) on the time-varying, three-dimensional flow structure of flat-plate wings rotating from rest at 45° angle of attack. Plates of Open image in new window = 2 and 4 are tested in a 50 % by mass glycerin–water mixture, with a total rotation of ϕ = 120° and a matched tip Reynolds number of 5,000. The time-varying, three-component volumetric velocity field is reconstructed using phase-locked, phase-averaged stereoscopic digital particle image velocimetry in multiple, closely-spaced chordwise planes. The vortex structure is analyzed using the \(\mathcal{Q}\)-criterion, helicity density, and spanwise quantities. For both Open image in new window s, the flow initially consists of a connected and coherent leading-edge vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the LEV increases in size with span and tilts aft. Smaller, discrete vortices are present in the separated shear layers at the trailing and tip edges, which wrap around the primary TEV and TV. After about ϕ = 20°, the outboard-span LEV lifts off the plate and becomes arch-like. A second, smaller LEV and the formation of corner vortex structures follow. For Open image in new window = 4, the outboard LEV moves farther aft, multiple LEVs form ahead of it, and after about ϕ = 50° a breakdown of the lifted-off LEV and the TV occurs. However, for Open image in new window = 2, the outboard LEV lift-off is not progressive, and the overall LEV-TV flow remains more coherent and closer to the plate, with evidence of breakdown late in the motion. Inboard of about 50 % span, the Open image in new window = 4 LEV is stable for the motion duration. Up to approximately 60 % span, the Open image in new window = 2 LEV is distinct from the TV and is similarly stable. The Open image in new window = 2 LEV exhibits substantially higher spanwise vorticity and velocity. The latter possesses a “four-lobed” distribution at the periphery of the LEV core having adjacent positive (outboard) and negative (inboard) components, corresponding to a helical streamline structure. Both Open image in new window s show substantial root-to-tip velocity aft of the stable LEV, which drives outboard spanwise vorticity flux; flux toward the root is also present in the front portion of the LEV. For Open image in new window = 2, there is a strong flux of spanwise vorticity from the outboard LEV to the tip, which may mitigate LEV lift-off and is not found for Open image in new window = 4. The TV circulation for each Open image in new window is similar in magnitude and growth when plotted versus the chord lengths travelled by the tip, prior to breakdown. Streamwise vorticity due to the TV induces high spanwise velocity, and for Open image in new window = 2, the tilted LEV creates further streamwise vorticity which corresponds well to spanwise-elongated regions of spanwise velocity. For Open image in new window = 2, the TV influences a relatively greater portion of the span and is more coherent at later times, which coupled with the tilted LEV strongly contributes to the higher overall spanwise velocity and vorticity flux.

Let Open image in new window be functors. We know that the class [F, G] of all functorial morphisms from F into G is not always a set, so that we can not speak in general about the category of all functors from Open image in new window into Open image in new window et. But instead of all functors from Open image in new window into Open image in new window we can consider only so-called proper functors, which were defined by Isbell [3]. In this way we can define a category Open image in new window , the category of all proper functors from Open image in new window into Open image in new window . This category contains Open image in new window as a full subcategory and it coincides with the category Open image in new window in the case when Open image in new window is a small category.

This paper examines the meanings, expressive functions, and semantic construal strategy of the adverbs bai ( Open image in new window ), gan ( Open image in new window ), xia ( Open image in new window ), kong ( Open image in new window ), xu ( Open image in new window ), tu ( Open image in new window ), and wang ( Open image in new window ) in Mandarin. We begin by discussing the original meaning of the adverbs through which their implicit negations are then depicted. Then, we explore the counter-expectative function of the implicit negative adverbs and match them with different verbs. The counter-expectation of these implicit negative adverbs were classified and categorized based on the speakers’intentions, which mainly discusses the semantic condition and construal strategy of implicit negative adverbs. Finally, the construal formula in logic and construal process is analyzed. We conclude that bai, gan, xia, kong, xu, tu, and wang in Mandarin have implicit meanings, which negate the felicity condition of an event. The implicit negative adverbs can express the counter-expectation of the speaker, indicating that the actual situation is different from what the speaker expected. Additionally, the semantic construal of the counter-expectation relates to the evaluative function of the event, which corresponds to the optimistic orientation of human beings. The semantic construal of the implicit negation in Mandarin can help process negative information in both machine translation and teaching Chinese as a foreign language.

We study the Open image in new window (shortly, Open image in new window ) problem on geometric intersection graphs such as interval, circular-arc, permutation, unit-disk, outer-string graphs, etc. Given a Open image in new window graph \(G=(V,E)\), where each vertex in V is colored with either “ Open image in new window ” or “ Open image in new window ”, the BCS problem seeks a maximum cardinality induced connected subgraph H of G such that H is Open image in new window , i.e., H contains an equal number of red and blue vertices. We study the computational complexity landscape of the BCS problem while considering geometric intersection graphs. On one hand, we prove that the BCS problem is NP-hard on the unit disk, outer-string, complete grid, and unit square graphs. On the other hand, we design polynomial-time algorithms for the BCS problem on interval, circular-arc and permutation graphs. In particular, we give algorithms for the Open image in new window problem on both interval and circular-arc graphs, and those algorithms are used as subroutines for solving the BCS problem on the same classes of graphs. Finally, we present a FPT algorithm for the BCS problem on general graphs.

The graph of an algebra A is the relational structure G(A) in which the relations are the graphs of the basic operations of A. Let denote by Open image in new window the class of all graphs of algebras from a class Open image in new window. We prove that if Open image in new window is a class of semigroups possessing a nontrivial member with a neutral element, then Open image in new window does not have finite quasi-equational basis. We deduce that, for a class Open image in new window of monoids or groups with a nontrivial member, Open image in new window also does not have finite quasi-equational basis.

In this paper we prove the Hyers-Ulam stability of the perfect linear differential equation f ( t ) y ″ ( t ) + f 1 ( t ) y ′ ( t ) + f 2 ( t ) y ( t ) = Q ( t ) , where f , y ∈ C 2 [ a , b ] , Q ∈ C [ a , b ] , f 2 ( t ) = f 1 ′ ( t ) − f ″ ( t ) and − ∞ < a < b < + ∞ . MSC:34K20, 26D10, 39B82, 34K06, 39B72.

The subject of this note is a characterization for the strong generator of a Ray resolvent. The discussion arose from the question if there exists any Hille-Yoshida type theorem in the context of Ray resolvents. More precisely the problem is the following: Given a compact space K and a linear operator L which maps a subspace of the space of continuous functions on K into , find necessary and sufficient conditions on (L, ) which ensure that L is the strong generator of a Ray resolvent on K.

Let ℚ denote the field of rational numbers, Open image in new window an algebraic closure of ℚ, and H : Open image in new window the absolute, multiplicative, Weil height. For each positive integer d and real number \( \mathcal{H} \geqslant 1 \), it is well known that the number Open image in new window of points α in Open image in new window having degree d over ℚ and satisfying \( H\left( \alpha \right) \leqslant \mathcal{H} \) is finite. This is the one-dimensional case of Northcott’s Theorem [8] (see also [5, page 59]). The systematic study of the counting function Open image in new window , and that of related functions in higher dimensions, was begun by Schmidt [10]. It is relatively easy to prove the existence of a positive constant C = C(d) such that Open image in new window (1) and also the existence of positive constants c = c(d) and \( \mathcal{H}_0 = \mathcal{H}_0 \left( d \right) \) such that Open image in new window (2)

We study Open image in new window , which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a given Stable Marriage or Stable Roommates instance is called Open image in new window if it does not admit any Open image in new window , that is, a subset S of agents in which everyone prefers the partner of some other agent in S. The matching is Open image in new window if it does not admit any Open image in new window , that is, an exchange-blocking coalition of size two.

Some 25 years ago Valiant introduced an algebraic model of computation in order to study the complexity of evaluating families of polynomials. The theory was introduced along with the complexity classes Open image in new window and Open image in new window which are analogues of the classical classes Open image in new window and Open image in new window . Families of polynomials that are difficult to evaluate (that is, Open image in new window -complete) includes the permanent and hamiltonian polynomials.

We study perfect zero-knowledge proofs ( Open image in new window ). Unlike statistical zero-knowledge, where many fundamental questions have been answered, virtually nothing is known about these proofs.We consider reductions that yield hard and complete problems in the statistical setting. The issue with these reductions is that they introduce errors into the simulation, and therefore they do not yield analogous problems in the perfect setting. We overcome this issue using an error shifting technique. This technique allows us to remove the error from the simulation. Consequently, we obtain the first complete problem for the class of problems possessing non-interactive perfect zero-knowledge proofs ( Open image in new window ), and the first hard problem for the class of problems possessing public-coin Open image in new window proofs.We get the following applications. Using the error shifting technique, we show that the notion of zero-knowledge where the simulator is allowed to fail is equivalent to the one where it is not allowed to fail. Using our complete problem, we show that under certain restrictions Open image in new window is closed under the OR operator. Using our hard problem, we show how a constant-round, perfectly hiding instance-dependent commitment may be obtained (this would collapse the round complexity of public-coin Open image in new window proofs to a constant).

Given Banach space operators A ∈ B( Open image in new window ) and B ∈ B( Open image in new window ), let A⊗B ∈ B( Open image in new window ⊗ Open image in new window ) denote the tensor product of A and B. Let σa, σaw and σab denote the approximate point spectrum, the Weyl approximate point spectrum and the Browder approximate point spectrum, respectively. Then σaw(A⊗B) ⊆ σa(A)σaw(B) ⊂ σaw(A)σa(B) ⊆ σa(A)σab(B) ⊂ σab(A)σa(B) = σab(A⊗B), and a sufficient condition for the (a-Weyl spectrum) identity σaw(A⊗B) = σa(A)σaw(B) ⊂ σaw(A)σa(B) to hold is that σaw(A⊗B) = σab(A⊗B). Equivalent conditions are proved in Theorem 1, and the problem of the transference of a-Weyl’s theorem for a-isoloid operators A and B to their tensor product A⊗B is considered in Theorem 2. Necessary and sufficient conditions for the (plain) Weyl spectrum identity are revisited in Theorem 3.

By labeling the structure of Analects of the Sixth Chan Patriarch Huineng, this paper is devoted to study of the explicit and implicit connectives, their semantics and usage. We examine the following results: 1) Implicit connectives (2067,84.9%) are more than explicit connectives (369,15.1%). Among 17 discourse relations, only in 2 Hypothesis and Concession explicit connectives are used more than implicit. 2) There are different ways to use synonymous connectives to represent the same relation. On the one hand, the connectives are used most frequently in Continuity – 14 times. On the other hand, Summary-elaboration and Background relations can be set up without any connectives. 3) Among 60 kinds of connectives, the monosemous connectives are more than the polysemous. Polysemous connectives (“ruo( Open image in new window ), ji( Open image in new window ), yi( Open image in new window )”) contain at most 4 meanings which are used in different ways in sentences. Besides, we analyze the usage of synonymous connectives in Hypothesis and the polysemous connective (“ji( Open image in new window )”) for case studies.