Explicit Version Research Articles

Examples and cofibrant generation of effective Kan fibrations

We will make two contributions to the theory of effective Kan fibrations, which are a more explicit version of the notion of a Kan fibration, a notion which plays a fundamental role in simplicial homotopy theory. We will show that simplicial Malcev algebras are effective Kan complexes and that the effective Kan fibrations can be seen as the right class in an algebraic weak factorization system. In addition, we will introduce two strengthenings of the notion of an effective Kan fibration, the symmetric effective and degenerate-preferring Kan fibrations, and show that the previous results hold for these strengthenings as well.

A note on (2,2)-isogenies via theta coordinates

In this paper, we revisit the algorithm for computing chains of (2,2)-isogenies between products of elliptic curves via theta coordinates proposed by Dartois et al. For each fundamental block of this algorithm, we provide an explicit inversion-free version. Besides, we exploit the technique of x-only ladder to speed up the computation of gluing isogeny. Finally, we present a mixed optimal strategy, which combines the inversion-elimination tool with the original methods together to execute a chain of (2,2)-isogenies.We make a cost analysis and present a concrete comparison between ours and the previously known methods for inversion elimination. Furthermore, we implement the mixed optimal strategy for benchmark. The results show that when computing (2,2)-isogeny chains with lengths of 126, 208 and 632, compared to Dartois, Maino, Pope and Robert's latest implementation, utilizing our techniques can reduce 9.7%, 9.5% and 9.6% multiplications over the base field Fp, respectively. Therefore, even for the updated version that employs their inversion-free algorithms, our tools still possess an advantage.

Analytic computation of the entanglement of formation for bipartite isotropic states using their symmetry

It is well-known that computing the entanglement of formation of a general bipartite state is a difficult task. We use the local symmetry of bipartite isotropic states in arbitrary dimensions to compute their entanglement of formation analytically. Our computation is an explicit and detailed version of the computation performed by Terhal et al [B. M. Terhal and K. G. H. Vollbrecht, Phys. Rev. Lett. 85, 2625 (2000)]. However, it is not just a review but we also have our contribution and novelty. For instance, we provide a rigorous proof for the entanglement of formation of two qutrit isotropic states and notably we give a proof supporting the conjecture proposed by Terhal et al about the entanglement of formation of bipartite isotropic states for the last range of allowed parameter values.

An explicit version of Chen’s theorem assuming the Generalized Riemann Hypothesis

An explicit version of Chen’s theorem assuming the Generalized Riemann Hypothesis

The projection algorithm for inverse quasi-variational inequalities with applications to traffic assignment and network equilibrium control problems

We consider a first-order dynamical system for solving inverse quasi-variational inequalities in finite dimensional spaces. Through an explicit time discrete version of the proposed dynamical system, we investigate the linear convergence of a projection algorithm under suitable conditions of parameters. Moreover, we investigate the application of inverse quasi-variational inequalities in traffic assignment problem and network equilibrium control problem. The numerical experiments for these practical problems confirm the linear convergence of the theoretical part. In particular, the obtained results provide a positive answer to an open question posted by S. Dey and S. Reich in Optimization, DOI: 10.1080/02331934.2023.2173525 (2023).

Numerically explicit estimates for the distribution of rough numbers

For x≥y>1 and u:=log⁡x/log⁡y, let Φ(x,y) denote the number of positive integers up to x free of prime divisors less than or equal to y. In 1950 de Bruijn [4] studied the approximation of Φ(x,y) by the quantityμy(u)eγxlog⁡y∏p≤y(1−1p), where γ=0.5772156... is Euler's constant andμy(u):=∫1uyt−uω(t)dt. He showed that the asymptotic formulaΦ(x,y)=μy(u)eγxlog⁡y∏p≤y(1−1p)+O(xR(y)log⁡y) holds uniformly for all x≥y≥2, where R(y) is a positive decreasing function related to the error estimates in the Prime Number Theorem. In this paper we obtain numerically explicit versions of de Bruijn's result.

Continuous Feed Grinding Milling Process of Soda-Lime Glass Using Smoothed-Particle Hydrodynamics

A smoothed-particle hydrodynamics (SPH) modeling technique was applied in conjunction with the Johnson–Holmquist (JH-2) ceramic material constitutive model to replicate the fracture of soda-lime glass in a milling manufacturing process. Four-point bending tests were conducted to validate the soda-lime glass bulk material properties prior to its implementation in ABAQUS CAE™ Explicit (Version 2017). The JH-2 material constitutive model replicated the fracture load and time to fracture for the four-point bending load cases as per ASTM C158. This study showed how SPH in combination with a validated JH-2 material model in a milling process simulation was able to replicate the output size distribution at 5000 and 6500 revolutions per minute (RPM). For operations at 3000 RPM or lower, it was shown that it is necessary to include additional effects in the model, such as fluid–structure interactions, to improve the correlation with the experimental data. The SPH model was validated through an experimental campaign using high-speed cameras and a particle Camsizer. The experimental results clearly indicate a direct relation between the mill’s RPM and the output particle size distribution.

Explicit bounds on ζ(s) in the critical strip and a zero-free region

We derive explicit upper bounds for the Riemann zeta-function ζ(σ+it) on the lines σ=1−k/(2k−2) for integer k≥4. This is used to show that the zeta-function has no zeroes in the regionσ>1−log⁡log⁡|t|21.233log⁡|t|,|t|≥3. This is the largest known zero-free region for exp⁡(171)≤t≤exp⁡(5.3⋅105). Our results rely on an explicit version of the van der Corput AnB process for bounding exponential sums.

An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes

Abstract We make explicit Bombieri’s refinement of Gallagher’s log-free “large sieve density estimate near σ = 1 {\sigma=1} ” for Dirichlet L-functions. We use this estimate and recent work of Green to prove that if N ≥ 2 {N\geq 2} is an integer, A ⊆ { 1 , … , N } {A\subseteq\{1,\ldots,N\}} , and for all primes p no two elements in A differ by p - 1 {p-1} , then | A | ≪ N 1 - 10 - 18 {|A|\ll N^{1-10^{-18}}} . This strengthens a theorem of Sárközy.

Two new classes of exponential Runge–Kutta integrators for efficiently solving stiff systems or highly oscillatory problems

We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study two new classes of exponential Runge–Kutta (ERK) integrators for efficiently solving stiff systems or highly oscillatory problems. We first present a novel class of explicit modified version of exponential Runge–Kutta (MVERK) methods based on the order conditions. Furthermore, we consider a class of explicit simplified version of exponential Runge–Kutta (SVERK) methods. Numerical results demonstrate the high efficiency of the explicit MVERK integrators and SVERK methods derived in this paper compared with the well-known explicit ERK integrators for stiff systems or highly oscillatory problems in the literature.

Spatially explicit Bayesian hierarchical models improve estimates of avian population status and trends

Abstract Population trend estimates form the core of avian conservation assessments in North America and indicate important changes in the state of the natural world. The models used to estimate these trends would be more efficient and informative for conservation if they explicitly considered the spatial locations of the monitoring data. We created spatially explicit versions of some standard status and trend models applied to long-term monitoring data for birds across North America. We compared the spatial models to simpler non-spatial versions of the same models, fitting them to simulated data and real data from 3 broad-scale monitoring programs: the North American Breeding Bird Survey (BBS), the Christmas Bird Count, and a collection of programs we refer to as Migrating Shorebird Surveys. All the models generally reproduced the simulated trends and population trajectories when there were many data, and the spatial models performed better when there were fewer data and in locations where the local trends differed from the range-wide means. When fit to real data, the spatial models revealed interesting spatial patterns in trend, such as recent population increases along the Appalachian Mountains for the Eastern Whip-poor-will (Antrostomus vociferus), that were much less apparent in results from the non-spatial versions. The spatial models also had higher out-of-sample predictive accuracy than the non-spatial models for a selection of species using BBS data. The spatially explicit sharing of information allows fitting the models with much smaller strata, allowing for finer-grained patterns in trends. Spatially informed trends will facilitate more locally relevant conservation, highlight areas of conservation successes and challenges, and help generate and test hypotheses about the spatially dependent drivers of population change.

AN EXPLICIT MEAN-VALUE ESTIMATE FOR THE PRIME NUMBER THEOREM IN INTERVALS

AbstractThis paper gives an explicit version of Selberg’s mean-value estimate for the prime number theorem in intervals, assuming the Riemann hypothesis [25]. Two applications are given to short-interval results for primes and for Goldbach numbers. Under the Riemann hypothesis, we show there exists a prime in $(y,y+32\,277\log ^2 y]$ for at least half the $y\in [x,2x]$ for all $x\geq 2$ , and at least one Goldbach number in $(x,x+9696 \log ^2 x]$ for all $x\geq 2$ .

The prime number theorem for primes in arithmetic progressions at large values

Abstract Assuming the Riemann hypothesis, we prove the latest explicit version of the prime number theorem for short intervals. Using this result, and assuming the generalised Riemann hypothesis for Dirichlet L-functions is true, we then establish explicit formulae for $\psi(x,\chi)$, $\theta(x,\chi)$ and an explicit version of the prime number theorem for primes in arithmetic progressions that hold for general moduli $q\geq 3$. Finally, we restrict our attention to $q\leq 10\,000$ and use an exact computation to refine these results.

How robust are egocentric and altercentric interference effects in social cognition? a test with explicit and implicit versions of a continuous false belief task.

It has been long assumed that meta-representational theory of mind (ToM) -our ability to ascribe mental states to ourselves and other people- emerges around age four as indicated in performance on explicit verbal false belief tasks. In contrast, newer studies assessing false belief understanding with implicit, non-verbal measures suggest that some form of ToM may be present even in infancy. But these studies now face replication issues, and it remains unclear whether they can provide robust evidence for implicit ToM. One line of research on implicit ToM, however, may remain promising: Studies that tap so-called altercentric biases. Such biases occur when agents in their judgments about the world are influenced (perform slower, more error-prone) in light of another agent's deviating perspective even if that perspective is completely irrelevant to the task; they thus can be seen as indicators of spontaneous and implicit ToM. Altercentric biases are the mirror images of egocentric biases (agents are influenced by their own perspective when evaluating another agent's deviating perspective). In three studies with adults, we aimed to tap both egocentric and altercentric interference effects within the same task format. We used the so-called Sandbox task, a false belief task with continuous locations. In Study 1, we tested an online adaptation of the Sandbox task, which we also used to explore potential cross-cultural differences in these biases. Studies 2 and 3 combined the Sandbox task with mouse-tracking measures. These studies revealed neither egocentric nor altercentric biases. These null results are discussed with regard to the question whether absence of evidence here may present evidence of absence of such spontaneous perspective-taking biases or merely false negatives.

Comparative Analysis of the Polygamy Regulations in Indonesia and Morocco

The purpose of this essay is to compare and comprehend the similarities and differences in the rules governing polygamy in the countries of Indonesia and Morocco. applying a normative strategy while also utilizing comparative research. Using secondary data sources and involving primary, secondary, and tertiary sources of legal information in the research process. Technique of analysis combined with content analysis. In light of this, the law in Morocco goes one step further in providing the wife the ability to create conditions or a marriage agreement, the objective of which is that she is not willing to be co-opted. Despite the fact that both parties subscribe to polygamy, the law in Morocco goes one step further. The court will not grant the spouse permission to remarry even if he expresses a desire to do so. In Indonesia, one does not find an explicit version of the same regulation. Aside from that, the legislation in Morocco seems to further scare men into not practicing polygamy by beginning the sound of various articles with the phrase "polygamy is prohibited if," and so on. This is done to discourage spouses from engaging in the practice. In spite of the fact that the law in Indonesia has a propensity to utilize forceful language, such as mandatory and must, etc. Learning about laws in other countries will broaden legal horizons in the future, especially when revising a law that requires amendments at some time. The benefit of this article is to know and understand the similarities and differences in the regulation of polygamy in Indonesia and Morocco. In addition, learning about laws in other countries will broaden legal horizons in the present.

Recent Advances of Indium Oxide-Based Catalysts for CO2 Hydrogenation to Methanol: Experimental and Theoretical.

Methanol synthesis from the hydrogenation of carbon dioxide (CO2) with green H2 has been proven as a promising method for CO2 utilization. Among the various catalysts, indium oxide (In2O3)-based catalysts received tremendous research interest due to the excellent methanol selectivity with appreciable CO2 conversion. Herein, the recent experimental and theoretical studies on In2O3-based catalysts for thermochemical CO2 hydrogenation to methanol were systematically reviewed. It can be found that a variety of steps, such as the synthesis method and pretreatment conditions, were taken to promote the formation of oxygen vacancies on the In2O3 surface, which can inhibit side reactions to ensure the highly selective conversion of CO2 into methanol. The catalytic mechanism involving the formate pathway or carboxyl pathway over In2O3 was comprehensively explored by kinetic studies, in situ and ex situ characterizations, and density functional theory calculations, mostly demonstrating that the formate pathway was extremely significant for methanol production. Additionally, based on the cognition of the In2O3 active site and the reaction path of CO2 hydrogenation over In2O3, strategies were adopted to improve the catalytic performance, including (i) metal doping to enhance the adsorption and dissociation of hydrogen, improve the ability of hydrogen spillover, and form a special metal-In2O3 interface, and (ii) hybrid with other metal oxides to improve the dispersion of In2O3, enhance CO2 adsorption capacity, and stabilize the key intermediates. Lastly, some suggestions in future research were proposed to enhance the catalytic activity of In2O3-based catalysts for methanol production. The present review is helpful for researchers to have an explicit version of the research status of In2O3-based catalysts for CO2 hydrogenation to methanol and the design direction of next-generation catalysts.

Primes between consecutive powers

This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between n155 and (n+1)155 for all n≥1. This result is in part obtained with a new explicit version of Goldston's 1983 estimate for the error in the truncated Riemann–von Mangoldt explicit formula.

Implicit to Explicit Algorithm for ABAQUS Standard User-Subroutine UMAT for a 3D Hashin-Based Orthotropic Damage Model

This study examines a new approach to facilitate the convergence of upcoming user-subroutines UMAT when the secant material matrix is applied rather than the conventional tangent (also known as Jacobian) material matrix. This algorithm makes use of the viscous regularization technique to stabilize the numerical solution of softening material models. The Newton–Raphson algorithm predictor-corrector of ABAQUS then applies this type of viscous regularization to a UMAT using only the secant matrix. When the time step is smaller than the viscosity parameter, this type of regularization may be unsuitable for a predictor-corrector with the secant matrix because its implicit convergence is incorrect, transforming the algorithm into an undesirable explicit version that may cause convergence problems. A novel 3D orthotropic damage model with residual stresses is proposed for this study, and it is analyzed using a new algorithm. The method’s convergence is tested using the proposed implicit-to-explicit secant matrix as well as the traditional implicit and explicit secant matrices. Furthermore, all numerical models are compared to experimental data. It was concluded that both the new 3D orthotropic damage model and the new proposed time step algorithm were stable and robust.

The Eisenstein and winding elements of modular symbols for odd square-free level

We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups \(\Gamma _0(N)\) with N odd square-free. We also compute the winding elements explicitly for these congruence subgroups. Our results are explicit versions of the Manin-Drinfeld Theorem [Thm. 6]. These results are the generalization of the paper [1] results to odd square-free level.

Atkinson's formula for the mean square of ζ(s) with an explicit error term

We provide an explicit O(log2⁡T)-term of the celebrated Atkinson's formula for the error term E(T) of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of well-known estimate E(T)≪εT13+ε.