Intermediate Property Research Articles

Beurling dimension of spectra for a class of random convolutions on [formula omitted]

It is usually difficult to study the structure of the spectra for the measures in R2 and higher dimensions. In this paper, by employing the projective techniques and our previous results on the line we prove that the Beurling dimension of spectra for a class of random convolutions in R2 satisfies an intermediate value property.

Parametric design and modeling method of carbon fiber reinforcement plastic-laminated components applicable for multi-material vehicle body development

Abstract Combined application of steel, aluminum, and carbon fiber reinforcement plastic (CFRP) is the main direction of future lightweight body development. However, the anisotropy and additional lamination design variables of CFRP parts pose significant challenges for the development of multi-material bodies. This study establishes a parametric design method for the variable-thickness lamination scheme based on non-uniform rational B-splines, it can be coupled with existing parametric design methods for structural shapes to formulate a complete parametric design and modeling of CFRP components. On this basis, a homogenized intermediate material property is derived from classic laminate theory by introducing lamination assumptions, it enables a stepwise multi-material body optimization method to solve the challenge that components’ material design variables switching between CFRP and alloy will introduce/eliminate lamination design variables iteratively, posing a great optimization convergence difficulty. The proposed parametric modeling method for CFRP components was validated by experimental tests of a fabricated roof beam, and the proposed optimization method was applied to a vehicle body, achieving 15.9%, 23.9%, 18.6%, and 12.2% increase in bending and torsional stiffness and modal frequencies; 20.2%, 9.3%, and 12.7% reduction of weight and peak acceleration in frontal and side collisions. This study enables the forward design of multi-material bodies compatible with CFRP parts.

Conditional intermediate entropy and Birkhoff average properties of hyperbolic flows

AbstractKatok [Lyapunov exponents, entropy and periodic points of diffeomorphisms. Publ. Math. Inst. Hautes Études Sci.51 (1980), 137–173] conjectured that every $C^{2}$ diffeomorphism f on a Riemannian manifold has the intermediate entropy property, that is, for any constant $c \in [0, h_{\mathrm {top}}(f))$ , there exists an ergodic measure $\mu $ of f satisfying $h_{\mu }(f)=c$ . In this paper, we obtain a conditional intermediate metric entropy property and two conditional intermediate Birkhoff average properties for basic sets of flows that characterize the refined roles of ergodic measures in the invariant ones. In this process, we establish a ‘multi-horseshoe’ entropy-dense property and use it to get the goal combined with conditional variational principles. We also obtain the same result for singular hyperbolic attractors.

On the intermediate value property of spectra for a class of Moran spectral measures

We prove that the Beurling dimensions of the spectra for a class of Moran spectral measures are in 0 and their upper entropy dimensions. Moreover, for such a Moran spectral measure μ, we show that the Beurling dimension for the spectra of μ has the intermediate value property: let t be any value in 0 and the upper entropy dimension of μ, then there exists a spectrum whose Beurling dimension is t. In particular, this result settles affirmatively a conjecture involving spectral Bernoulli convolution in Fu et al. (2018) [20]. Furthermore, we prove that the set of the spectra whose Beurling dimensions are equal to any fixed value in 0 and dim‾eμ has the cardinality of the continuum.

On convexity properties with respect to a Chebyshev system

The main purpose of this paper is to introduce various convexity concepts in terms of a positive Chebyshev system ω and give a systematic investigation of the relations among them. We generalize a celebrated theorem of Bernstein–Doetsch to the setting of ω-Jensen convexity. We also give sufficient conditions for the existence of discontinuous ω-Jensen affine functions. The concept of Wright convexity is extended to the setting of Chebyshev systems, as well, and it turns out to be an intermediate convexity property between ω-convexity and ω-Jensen convexity. For certain Chebyshev systems, we generalize the decomposition theorems of Wright convex and higher-order Wright convex functions obtained by C. T. Ng in 1987 and by Maksa and Páles in 2009, respectively.

Superluminal propagation from IR physics

One may believe that front velocities of waves in a given theory coincide with the UV limit of phase velocities for any dispersion relations. This implies that IR physics is irrelevant to the discussion of propagation speed of waves. We first consider a theory that contains higher spatial derivatives in the wave equation and prove that front velocities coincide with the UV limit of phase velocities, at least, if parity is conserved. However, we also show that front velocities do not coincide with the UV limit of phase velocities in general dispersion relations. We explicitly give several examples in which front velocities are superluminal owing to an IR or intermediate energy scale property of dispersion relations even if the UV limit of phase velocities is luminal. Our finding conveys the important caution that not only UV physics but also IR physics can be significant to superluminality.

FRACTAL DIMENSIONS OF SETS DEFINED BY DIGIT RESTRICTIONS IN ℝ2

We introduce a class of sets defined by digit restrictions in [Formula: see text] and study its fractal dimensions. Let [Formula: see text] be a set defined by digit restrictions in [Formula: see text]. We obtain the Hausdorff and lower box dimensions of [Formula: see text]. Under some condition, we gain the packing and upper box dimensions of [Formula: see text]. We get the Assouad dimension of [Formula: see text] and show that it is 2 if and only if [Formula: see text] contains arbitrarily large arithmetic patches. Under some conditions, we study the upper spectrum, quasi-Assouad dimension and Assouad spectrum of [Formula: see text]. Finally, we give an intermediate value property of fractal dimensions of the class of sets.

On the quasi-Beurling dimensions of the spectra for planar Moran-type Sierpinski spectral measures

We prove that the quasi-Beurling dimension of the spectra of planar Moran-type Sierpinski spectral measure μ satisfies an intermediate value property, i.e., for any t ∈ [ 0 , dim ‾ e μ ] , there exists a spectrum Λ t of μ such that dim q B ⁡ Λ t = t , where dim ‾ e μ denotes the upper entropy dimension of μ and dim q B ⁡ Λ t denotes the quasi-Beurling dimension of Λ t .

Conductivity gain predictions for multiscale fibrous composites with interfacial thermal barrier resistance

Nanocomposites are heterogeneous media with two or more micro‐structural levels. For instance, a nano‐level is characterized by isolated nano‐inclusions, and a micro‐level is represented by the clusters resulting from aggregation processes. Based on the reiterated homogenization method, we present a procedure to study the influence of this aggregation process and interfacial thermal resistance on the effective thermal conductivity for 2‐D square arrays of circular cylinders. First, an effective intermediate thermal property is obtained by taking into account only the influence of the individual nano‐inclusions in the matrix. Second, the final effective thermal coefficient ( ) is calculated considering the clusters immersed in the intermediate effective medium derived in the first step. The conductivity gain ( ) is defined as the quotient ( ) where is the effective thermal coefficient computed considering only one microstructural level with the same volumetric fraction of inclusions. We apply the theory of complex variable functions deriving in an infinite system of equations solvable by truncation method. The analytical formulas of the effective coefficient used in the calculations generalize other well‐known formulas reported in the literature. We also provide formulas for several truncation orders. The main novel contribution is in the reiterative application of the obtained formulas to illustrate the gain effect in nanocomposites, expressed as a function of the Biot number, thermal conductivities, volumetric fibers fraction, and an aggregation parameter. Furthermore, this result can be used to assess numerical computations and for nano‐reinforced fibers and nanofluids applications. An appendix is included showing similarities and differences with a three‐phase model.

Contextuality degree of quadrics in multi-qubit symplectic polar spaces

Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker Theorem, we formulate the contextuality property as the absence of solutions to a linear system and define for a contextual configuration its degree of contextuality. Then we explain why subgeometries of binary symplectic polar spaces are candidates for contextuality proofs. We report the results of a software that generates these subgeometries, decides their contextuality and computes their contextuality degree for some small symplectic polar spaces. We show that quadrics in the symplectic polar space W n are contextual for . The proofs we consider involve more contexts and observables than the smallest known proofs. This intermediate size property of those proofs is interesting for experimental tests, but could also be interesting in quantum game theory.

Remarks on the infinite‐dimensional counterparts of the Darboux theorem

The Darboux theorem, one of the fundamental results in analysis, states that the derivative of a real (not necessarily continuously) differentiable function defined on a compact interval has the intermediate value property, that is, attains each value between the derivatives at the endpoints. The Bolzano intermediate value theorem, which implies Darboux's theorem when the derivative is continuous, states that a continuous real‐valued function defined on satisfying and , has a zero, that is, for at least one number . It has numerous counterparts in multivariate calculus as well as in the infinite‐dimensional setting. The present paper is devoted to the discussion of some infinite‐dimensional variants of the Darboux theorem, which does not seem to be sufficiently deeply discussed. The study relies on different notions of nonsmooth differentiability of real functions and some appropriate compactness conditions. Problems involving functionals bounded below, monotone operators, and some general questions concerning the existence of the so‐called generalized equilibria are discussed.

Complex-analytic intermediate hyperbolicity, and finiteness properties

Motivated by the finiteness of the set of automorphisms Aut([Formula: see text]) of a projective manifold of general type [Formula: see text], and by Kobayashi–Ochiai’s conjecture that a projective manifold dim([Formula: see text])-analytically hyperbolic (also known as strongly measure hyperbolic) should be of general type, we investigate the finiteness properties of Aut([Formula: see text]) for a complex manifold satisfying a (pseudo-) intermediate hyperbolicity property. We first show that a complex manifold [Formula: see text] which is (dim([Formula: see text])-1)-analytically hyperbolic has indeed finite automorphisms group. We then obtain a similar statement for a pseudo-(dim([Formula: see text])-1)-analytically hyperbolic, strongly measure hyperbolic projective manifold [Formula: see text], under an additional hypothesis on the size of the degeneracy set. Some of the properties used during the proofs lead us to introduce a notion of intermediate Picard hyperbolicity, which we last discuss.

The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation

On taking the intermediate value theorem (IVT) and its converse as a point of departure, this paper connects the intermediate value property (IVP) to the continuity postulate typically assumed in mathematical economics, and to the solvability axiom typically assumed in mathematical psychology. This connection takes the form of four portmanteau theorems, two for functions and the other two for binary relations, that give a synthetic and novel overview of the subject. In supplementation, the paper also surveys the antecedent literature both on the IVT itself, as well as its applications in economic and decision theory. The work underscores how a humble theorem, when viewed in a broad historical frame, bears the weight of many far-reaching consequences; and testifies to a point of view that the apparently complicated can sometimes be under-girded by a most basic and simple execution.

Synthesis, photoluminescence, and up-conversion luminescence properties of YTiTaO6:Er3+/Yb3+

The relationship between the factors (i.e. the concentrations of Yb3+ and Er3+ and heating temperature in air) and the properties of photoluminescence (PL) and up-conversion luminescence of YTiTaO6:Er3+/Yb3+ whose crystalline phase depended on heating temperature in air was examined using samples synthesized hydrothermally. The intense green emission (: 2H11/2,4S3/2→4I15/2 transitions of Er3+) was obtained by the excitation at 288 ​nm using the indirect energy transfer from the YTiTaO6 host crystal, which was about 1.8 times stronger than that obtained by the direct excitation at 380 ​nm via the f-f transition (: 4I15/2→4G11/2) of Er3+. Aeschynite phase exhibited intermediate luminescence property. The up-conversion emission intensity increased with increasing heating temperature and became the maximum at x ​= ​0.10 and y ​= ​0.20 with euxenite phase, although the co-presence of Yb3+ gave negative effect on the PL intensity of ErxYbyY1-x-yTiTaO6. As heating temperature rose to 1300–1400 ​°C the intensity of the red up-conversion emission (: 4F9/2→4I15/2 transition) became greater than that of the green emission (: 4S3/2→4I15/2 transition), accordingly the position of the color chromaticity coordinates shifted slightly from green to yellow.

On a differential intermediate value property

Liouville closed $H$-fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order $1$ has a nontrivial solution. (The introduction gives a precise definition.) For a Liouville closed $H$-field $K$ with small derivation we show: $K$ has the Intermediate Value Property for differential polynomials iff $K$ is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.

Ergodic Optimization and Zero Temperature Limits in Negative Curvature

In this paper, we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. In topological dynamics, it is a well-known fact that every continuous potential on a compact metric space has a maximizing measure. Unfortunately, for non-compact spaces this fact is no longer true. For the geodesic flow we provide a criterion that ensures the existence of a maximizing measure for uniformly continuous potentials. We prove that the only obstruction to the existence of a maximizing measure is the full escape of mass phenomenon. To the best of our knowledge, this is the first general result on the existence of maximizing measures for non-compact topological spaces which does not require the potential to be coercive. We study zero temperature limits of equilibrium measures for a suitable family of potentials. We prove some convergence and divergence results for the limiting behavior of such measures. Among some consequences, we obtain that the geodesic flow has the intermediate entropy property and that equilibrium states are dense in the space of invariant probability measures.

China’s Fair Competition Review System: A Single Case Study

The case study methodology has proved to be a useful empirical tool for competition policy evaluation. However, as far as China’s Fair Competition Review System (FCRS) is concerned, empirical studies are scarce. This article aims to partly fill this gap by thoroughly studying the first litigation case in light of three questions: (1) does China’s FCRS contribute to a competitive market?; (2) does it face challenges regarding implementation, including judicial proceedings?; and (3) how to tackle these challenges? We find that China’s FCRS promotes a competitive market to some extent, but diverse issues need to be tackled in the coming years. Some policymakers still lack understanding of the system. Public antitrust enforcement also faces understanding and capability problems to fully implement the FCRS. The review standards are not specific enough. Regarding judicial scrutiny of the FCRS, we note that also judges lack knowledge of the FCRS, especially in primary courts. Court jurisdictions for filing administrative monopoly litigation are not of high enough rank. In addition, the nature of the FCRS brings up doubts when entering into litigation as the case has to be connected with the Anti-Monopoly Law (AML). Consequently, we formulate several suggestions for improvement: First, strengthening competition advocacy and FCRS training for policymakers, antitrust enforcement officials, and judges. Second, establishing disciplinary and incentive mechanisms. Third, increasing enforcement capacity. Fourth, specifying industry-specific review standards. In terms of judicial scrutiny, in addition to the training for judges, we also propose to reform the administrative proceeding system, adding corresponding clauses connected to Chapter V of the AML and the FCRS into the Administrative Procedure Law. Abstract administrative actions should also have the possibility to initiate litigation in the near future, and administrative monopoly cases should be filed at least to an intermediate court or intellectual property court, rather than to a primary court. The establishment of a dedicated competition court could also add value. Last, we recommend upgrading the FCRS to proper law. China, Fair Competition Review System, Evaluation, Case study, Administrative monopoly

Local and global robustness at steady state

We study the robustness of the steady states of a class of systems of autonomous ordinary differential equations (ODEs), having as a central example those arising from (bio)chemical reaction networks. More precisely, we study under what conditions the steady states of the system are contained in a parallel translate of a coordinate hyperplane. To this end, we focus mainly on ODEs consisting of generalized polynomials and make use of algebraic and geometric tools to relate the local and global structure of the set of steady states. Specifically, we consider the local property termed zero sensitivity at a coordinate xi, which means that the tangent space is contained in a hyperplane of the form xi = c, and provide a criterion to identify it. We consider the global property termed absolute concentration robustness (ACR), meaning that all steady states are contained in a hyperplane of the form xi = c. We clarify and formalize the relation between the two approaches. In particular, we show that ACR implies zero sensitivity and identify when the two properties do not agree, via an intermediate property we term local ACR. For families of systems arising from modeling biochemical reaction networks, we obtain the first practical and automated criterion to decide upon (local) ACR.

Facile synthesis of the chemically oxidative grafted copolymer of 2,6-diaminopyridine (DAP) and thiophene (Th) for optoelectronic and antioxidant studies

The conjugated polymers-based graft copolymer is significantly explored due to their potential applications in sensing devices posing with notable optical and physiological properties. The current preliminary investigation presents for the first time the synthesis of grafted copolymer Poly (DAP-g-Th) from 2,6-diaminopyridine (DAP) and thiophene (Th) via chemical oxidative copolymerization using ferric chloride as an oxidizing agent for enhancing its photoluminescence properties. Modifications via copolymerization were confirmed by optical, morphological, and spectral analysis through FT-IR, UV-Visible, XRD, fluorescence studies. Increased value of oscillator strength, molar extinction coefficient, and lowered bandgap were observed in the case of poly(DAP-g-Th). FT-IR results showing alteration in the properties of polymer lying intermediate between individual monomers confirming copolymerization. Intermediate quantum yield value disclosing transformations in the electronic structure of the poly(DAP-g-Th). Morphological studies also suggested the intermediate property of copolymer. Poly(DAP-g-Th) showed the best antioxidant activity against DPPH free radical assay and its IC50 value was reported 0.024 ± 0.001 mg/ml.

Mechanism of improved intermediate temperature plasticity of nickel-base single crystal superalloy with hot isostatic pressing

In this work, we investigate the effect of hot isostatic pressing on the intermediate temperature tensile property of nickel-base single crystal superalloy. The experimental results indicate that the hot isostatic pressing improves the intermediate temperature plasticity of single crystal superalloy from 6.4% to 9.3%, but the yield strength remains unchanged. In addition, the fracture surface is changed by hot isostatic pressing, the microporosities disappear in the fracture surface under hot isostatic pressing, and an initial crack is formed from the region of plenty of stacked slip planar instead of microcracks by microporosities. The mechanism of the improvement of plasticity and the change of fracture behavior is explored in detail. The application of hot isostatic pressing reduces the size and volume faction of microporosities, which makes it difficult for the crack initiation and propagation, and further leads to the improvement of plasticity.