Formula For Density Research Articles

ẢNH HƯỞNG ĐỒNG THỜI CỦA HÌNH THỨC VÀ MẬT ĐỘ NUÔI TỚI TỈ LỆ SỐNG, SINH TRƯỞNG, NĂNG SUẤT VÀ HIỆU QUẢ KINH TẾ CỦA TU HÀI (Lutraria rhynchaena) TẠI VÂN ĐỒN, TỈNH QUẢNG NINH

This study was conducted to evaluate the effects of farming methods and density on the survival rate, growth, yeild and economic efficency of commercial otter clam in the sea waters of Van Don, Quang Ninh. The otter clams with an initial length of 18,36 mm and an average body weight of 4,12 g were used in this study. Two farming methods were arranged: cage culture (basket) hanging on the raft (including experiments TN1, TN2, TN3 and TN4) and cage culture placed on tidal flats (including experiments TN5, TN6, TN7 and TN8). For each culture, there were 4 formulas for stocking density of 25 individuals\cage (100 individuals\m2) (TN1, TN5), 35 individuals\cage (140 individuals\m2) (TN2, TN6); 45 individuals\cage (180 individuals\m2) (TN3, TN7); and 55 individuals\cage (220 individuals\m2) (TN4, TN8). Each treatment was triplicate and lasted for 12 months, the results showed that the density and farming methods had different effects on growth, survival rate and yield of commercial otter clam. The weight of the commercial otter clam ranged from 28,76 to 41,74 g\individual, the length varied from 51,17 to 72,69 mm\individual, and the survival rate fluctuated from 57,4 to 78,3%. The highest growth was recorded in the TN1 with density of 25 individuals\cage, the difference between treatments was statistically significant (p≤ 0.05). The average yield of commercial otter clam increased with the increase of stocking density, ranging from 21,7 to 38,3 tons\ha, the difference was statistically significant (p≤ 0,05). However, economic accounting showed that the economic efficiency was highest in TN2, the ottet clams were arranged in the cage hanging on rafts and stocking at a density of 35 individuals\cage (140 individuals\m2). In this experiment, the average growth in weight was 38,91 g\individual and in length was 68,47 mm\individual, the survival rate was 76,4%, and the yield was 32,9 tons\ha the economic profit reached 0,883 billion of Vietnam Dong and the profit rate reached 28,1, respectively. Based on these research results, it could be recommended to farmers to stock the otter clam with a density of 35 individuals\cage.

The Confidence Density for Correlation

Inference for correlation is central in statistics. From a Bayesian viewpoint, the final most complete outcome of inference for the correlation is the posterior distribution. An explicit formula for the posterior density for the correlation for the binormal is derived. This posterior is an optimal confidence distribution and corresponds to a standard objective prior. It coincides with the fiducial introduced by R.A. Fisher in 1930 in his first paper on fiducial inference. C.R. Rao derived an explicit elegant formula for this fiducial density, but the new formula using hypergeometric functions is better suited for numerical calculations. Several examples on real data are presented for illustration. A brief review of the connections between confidence distributions and Bayesian and fiducial inference is given in an Appendix.

Intersection complexes and unramified 𝐿-factors

Let X X be an affine spherical variety, possibly singular, and L + X \mathsf L^+X its arc space. The intersection complex of L + X \mathsf L^+X , or rather of its finite-dimensional formal models, is conjectured to be related to special values of local unramified L L -functions. Such relationships were previously established in Braverman–Finkelberg–Gaitsgory–Mirković for the affine closure of the quotient of a reductive group by the unipotent radical of a parabolic, and in Bouthier–Ngô–Sakellaridis for toric varieties and L L -monoids. In this paper, we compute this intersection complex for the large class of those spherical G G -varieties whose dual group is equal to G ˇ \check G , and the stalks of its nearby cycles on the horospherical degeneration of X X . We formulate the answer in terms of a Kashiwara crystal, which conjecturally corresponds to a finite-dimensional G ˇ \check G -representation determined by the set of B B -invariant valuations on X X . We prove the latter conjecture in many cases. Under the sheaf–function dictionary, our calculations give a formula for the Plancherel density of the IC function of L + X \mathsf L^+X as a ratio of local L L -values for a large class of spherical varieties.

Relationship between Quantum Physics and Maxwell’s Equations in the Model of a Hydrogen Atom

An attempt to bring together two different theories – classical electrodynamics and quantum mechanics is made. On the example of a hydrogen atom the problem of the hypothetic electron fall into a nucleus by means of the energy conservation law is examined. The essence of the present approach consists in the assumption, that the energy and momentum of an electron in quantum model are proportional to corresponding electromagnetic fluxes. In order to achieve the result, the new formula of momentum flux density not using Poynting vector was proposed. It states that the momentum flux depends not only on electric and magnetic components of the field, but also on a frequency of an electromagnetic wave. As the main result, it was demonstrated that the total including annihilation energy of an electron in Bohr’s atom model is equal to energy of a free electron mc2 without any mention of Relativity. An electromagnetic field inside an atom occurs quantized for each electron orbit. An additional consequence shows that the two fundamental definitions of quantum energy mc2 and ħω are interrelated. If ħω is admitted according to quantum physics, then mc2 follows automatically and vice versaю

Characteristics of Attention Bias in Patients With Depression Disorder, and the Influence of High Frequency Transcranial Magnetic Stimulation Therapy on the Attention Bias

We propose a general model to entirely describe XPM effects induced by 16QAM channels in hybrid QPSK/16QAM wavelength division multiplexed (WDM) systems. A power spectral density (PSD) formula is presented to predict the statistical properties of XPM effects at the end of dispersion management (DM) fiber links. We derive the analytical expression of phase error variance for optimizing block length of QPSK channel coherent receiver with decision-aided (DA) maximum-likelihood (ML) phase estimation (PE). With our theoretical analysis, the optimum block length can be employed to improve the performance of coherent receiver. Bit error rate (BER) performance in QPSK channel is evaluated and compared through both theoretical derivation and Monte Carlo simulation. The results show that by using the DA-ML with optimum block length, bit signal-to-noise ratio (SNR) improvement over DA-ML with fixed block length of 10, 20 and 40 at BER of 10−3 is 0.18 dB, 0.46 dB and 0.65 dB, respectively, when in-line residual dispersion is 0 ps/nm.

High-Performance Flexible Asymmetric Supercapacitor Paired with Indanthrone@Graphene Heterojunctions and MXene Electrodes.

The energy density formula illuminated that widening the voltage window and maximizing capacitance are effective strategies to boost the energy density of supercapacitors. However, aqueous electrolyte-based devices generally afford a voltage window less than 1.2 V in view of water electrolysis, and chemically converted graphene yields mediocre capacitance. Herein, multi-electron redox-reversible, structurally stable indanthrone (IDT) π-backbones were rationally coupled with the reduced graphene oxide (rGO) framework to form IDT@rGO molecular heterojunctions. Such conductive agent- and binder-free film electrodes delivered a maximized capacitance of up to 345 F g-1 in a potential range of -0.2 to 1.0 V. The partner film electrode-Ti3C2Tx MXene which worked in the negative potential range of -0.1 to -0.6 V-afforded a capacitance as large as 769 F g-1. Thanks to the perfect complementary potentials of the IDT@rGO heterojunction positive electrode and Ti3C2Tx MXene negative partner, the polyvinyl alcohol/H2SO4 hydrogel electrolyte-based flexible asymmetric supercapacitor delivered an enlarged voltage window of 1.6 V and an impressive energy density of 17 W h kg-1 at a high power density of 8 kW kg-1, plus remarkable rate capability and cycling life (capacitance retention of ∼90% after 10000 cycles) as well as exceptional flexibility and bendability.

Enormous Promotion of Photocatalytic Activity through the Use of Near-Single Layer Covalent Organic Frameworks

Enormous Promotion of Photocatalytic Activity through the Use of Near-Single Layer Covalent Organic Frameworks

Scattering in Quantum Dots via Noncommutative Rational Functions

In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via Nll M channels, the density rho of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio phi := N/Mle 1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit phi rightarrow 0, we recover the formula for the density rho that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any phi <1 but in the borderline case phi =1 an anomalous lambda ^{-2/3} singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.

Low Ionosphere under Influence of Strong Solar Radiation: Diagnostics and Modeling

Solar flares (SFs) and intense radiation can generate additional ionization in the Earth’s atmosphere and affect its structure. These types of solar radiation and activity create sudden ionospheric disturbances (SIDs), affect electronic equipment on the ground along with signals from space, and potentially induce various natural disasters. Focus of this work is on the study of SIDs induced by X-ray SFs using very low frequency (VLF) radio signals in order to predict the impact of SFs on Earth and analyze ionosphere plasmas and its parameters. All data are recorded by VLF BEL stations and the model computation is used to obtain the daytime atmosphere parameters induced by this extreme radiation. The obtained ionospheric parameters are compared with results of other authors. For the first time we analyzed physics of the D-region—during consecutive huge SFs which continuously perturbed this layer for a few hours—in detail. We have developed an empirical model of the D-region plasma density and gave a simple approximative formula for electron density.

The globalization theorem for the Curvature-Dimension condition

The Lott–Sturm–Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition locally: an essentially non-branching metric-measure space (X,mathsf {d},{mathfrak {m}}) (so that (text {supp}({mathfrak {m}}),mathsf {d}) is a length-space and {mathfrak {m}}(X) < infty ) verifying the local Curvature-Dimension condition {mathsf {CD}}_{loc}(K,N) with parameters K in {mathbb {R}} and N in (1,infty ), also verifies the global Curvature-Dimension condition {mathsf {CD}}(K,N). In other words, the Curvature-Dimension condition enjoys the globalization (or local-to-global) property, answering a question which had remained open since the beginning of the theory. For the proof, we establish an equivalence between L^1- and L^2-optimal-transport–based interpolation. The challenge is not merely a technical one, and several new conceptual ingredients which are of independent interest are developed: an explicit change-of-variables formula for densities of Wasserstein geodesics depending on a second-order temporal derivative of associated Kantorovich potentials; a surprising third-order theory for the latter Kantorovich potentials, which holds in complete generality on any proper geodesic space; and a certain rigidity property of the change-of-variables formula, allowing us to bootstrap the a-priori available regularity. As a consequence, numerous variants of the Curvature-Dimension condition proposed by various authors throughout the years are shown to, in fact, all be equivalent in the above setting, thereby unifying the theory.

Energy Density Theory of Lithium-Ion Capacitors

As a new generation of capacitors, lithium-ion capacitors (LICs) have the same power density and cycle life as traditional electric double-layer capacitors, and 2–5 times the energy density. For the first time, in this paper we derive the mathematical formulas for the energy density of LICs. These formulas describe the relationship between the energy density of LICs and all the critical parameters, including the specific capacities of anode (negative) and cathode (positive) electrodes, the capacity ratio of anode to cathode electrodes, the maximum and minimum voltages of the LICs, the specific capacity of pre-lithiation source and the degree of the pre-lithiation and so on. These formulas provide not only a clear direction for future research in materials and devices of LICs, but also a useful tool for LIC design.

Exchange Current Density of Solid Oxide Electrolysis Cell Electrodes

Introduction Numerical simulation is a powerful technique in evaluating solid oxide fuel cell (SOFC) performance. Such method enables to visualize SOFC performance e.g. in using new materials. It is also desirable to develop such method that visualizes internal phenomena in solid oxide electrolysis cell (SOEC). While various parameters are important in simulating phenomena in SOEC stacks, we focus on exchange current density (1,2). Here, exchange current density is experimentally measured and evaluated using single SOEC / SOFC reversible cells. Furthermore, the exchange current density for different electrode materials in both SOEC and SOFC operation modes is examined. Exchange current density is defined as the current exchanged at the electrode/electrolyte interfaces in both directions in equilibrium and thus , so that an identical value for a given electrode has to be obtained in both SOFC and SOEC modes. However, as such values are practically measured by applying certain current in opposite directions, apparent exchange current density measured could be somehow different due to various irreversible processes at the electrode/electrolyte interfaces. In this study, such apparent exchange current density values are obtained and discussed. Experimental In this study, we evaluated the exchange current densities of solid oxide cells with three types of fuel electrodes (A-1, 2, 3) and two types of air electrodes (B-1, 2). The exchange current densities were measured in the SOFC and SOEC modes using following materials: (A-1) Ni-ScSZ (NiO-ScSZ (ScSZ: 10mol%Sc2O3-1mol%CeO2-89mol%ZrO2)), (A-2) Rh-GDC (La0.1Sr0.9TiO3, Gd0.1Ce0.9O2, volume ratio 50:50 (LST-GDC), Rh 0.178 mg/cm2 supported on LST-GDC) co-impregnated material, and (A-3) Ni-GDC (Ni 0.167 mg/cm2 supported on LST-GDC) co-impregnated material for the fuel electrode; (B-1) LSCF/GDC ((La0.6 Sr0.4)(Co0.2 Fe0.8)O3/GDC), and (B-2) LSM ((La0.8Sr0.2)0.98MnO3) for the air electrode. The exchange current density was derived using the Butler-Volmer-type equation. The exchange current density obtained was fitted by the commonly used phenomenological formula of the exchange current density. We compared the obtained parameters and the dependencies on gas partial pressure. Results and Discussion Here, the differences in exchange current density at the fuel electrode are examined. Figure 1 shows the exchange current density as a function of humidity in the fuel, and fitted curves. The fitted curves of exchange current densities are almost similar in the SOFC and SOEC modes. However, the maximum value measured in the SOFC mode shown in Fig. 1 (b) was somehow higher than that measured in the SOEC mode shown in Fig. 1 (a). The difference in using the Ni-ScSZ fuel electrode was more remarkable than that using the Rh-GDC co-impregnated fuel electrode shown in Figs. 1 (c) and (d). It may be possible that the apparent exchange current density at the fuel electrode could include influences of irreversible processes, associated with steam electrolysis. The dependence of exchange current density on gas partial pressure (3) will be examined to discuss electrode processes in steam electrolysis. The exchange current density obtained in this study enables various simulations for SOECs, besides SOFCs. References T. Yonekura, Y. Tachikawa, T. Yoshizumi, Y. Shiratori, K. Ito, and K. Sasaki, ECS Trans., 35 (1), 1007-1014 (2011).K. Takino, Y. Tachikawa, K. Mori, S. M. Lyth, Y. Shiratori, S. Taniguchi, and K. Sasaki, Int. J. Hydrogen Energy, 45 (11), 6912-6925 (2020).T. Hosoi, T. Yonekura, K. Sunada, and K. Sasaki, J Electrochem Soc., 162 (1), F136-F152 (2015). Figure 1

Transitions in random graphs of fixed degrees with many short cycles

We analyze maximum entropy random graph ensembles with constrained degrees, drawn from arbitrary degree distributions, and a tuneable number of three-cycles (triangles). We find that such ensembles generally exhibit two transitions, a clustering and a shattering transition, separating three distinct regimes. At the clustering transition, the graphs change from typically having only isolated cycles to forming cycle clusters. At the shattering transition the graphs break up into many small cliques to achieve the desired three-cycle density. The locations of both transitions depend nontrivially on the system size. We derive a general formula for the three-cycle density in the regime of isolated cycles, for graphs with degree distributions that have finite first and second moments. For bounded degree distributions we present further analytical results on cycle densities and phase transition locations, which, while non-rigorous, are all validated via MCMC sampling simulations. We show that the shattering transition is of an entropic nature, occurring for all three-cycle density values, provided the system is large enough.

Partition-theoretic formulas for arithmetic densities, II

In earlier work generalizing a 1977 theorem of Alladi, the authors proved a partition-theoretic formula to compute arithmetic densities of certain subsets of the positive integers N as limiting values of q-series as q → ζ a root of unity (instead of using the usual Dirichlet series to compute densities), replacing multiplicative structures of N by analogous structures in the integer partitions P. In recent work, Wang obtains a wide generalization of Alladi's original theorem, in which arithmetic densities of subsets of prime numbers are computed as values of Dirichlet series arising from Dirichlet convolutions. Here the authors prove that Wang's extension has a partition-theoretic analogue as well, yielding new q-series density formulas for any subset of N. To do so, we outline a theory of q-series density calculations from first principles, based on a statistic we call the "q-density" of a given subset. This theory in turn yields infinite families of further formulas for arithmetic densities.

The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in mathbb {F}_{q}[T

In this paper, we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of L-functions. We also adapt to the function field setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of L-functions. Specifically, the focus of this paper is on the family of quadratic Dirichlet L-functions L(s,chi _{P}) where the character chi is defined by the Legendre symbol for polynomials in mathbb {F}_{q}[T] with mathbb {F}_{q} a finite field of odd cardinality, and the averages are taken over all monic and irreducible polynomials P of a given odd degree. As an application, we also compute the formula for the one-level density for the zeros of these L-functions.

Moments Calculation for the Doubly Truncated Multivariate Normal Density

In the present article, we derive an explicit expression for the truncated mean and variance for the multivariate normal distribution with arbitrary rectangular double truncation. We use the moment generating approach of Tallis (1961) and extend it to general μ, Σ and all combinations of truncation. As part of the solution, we also give a formula for the bivariate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after truncation. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.

Efficiency enhancement of an updated solar-driven intermediate band thermoradiative device

A novel model of the solar-driven intermediate band thermoradiative device consisting of a solar concentrator, an absorber, an intermediate band thermoradiative cell and an optical filter is proposed. The formulas of the power output density and efficiency are derived analytically. The device performances are optimized and the parametric selection criteria are provided. The maximum efficiency of the device operating in the optimal state reaches 23.1% and increases of 25.5% if compared with that of a thermoradiative solar cell without the intermediate band. It means that the intermediate band has a great effect on the systemic performance improvement. It is very significant to find that the proposed device can attain a large efficiency under a low concentration factor and the performance of the device is much better than that of the normal thermoradiative solar cell without the intermediate band and optical filter. Solar-driven intermediate band thermoradiative devices are worthy of research and development.

Product Matrix Processes With Symplectic and Orthogonal Invariance via Symmetric Functions

Abstract We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald processes introduced by Borodin and Corwin. Through this connection, we obtain explicit formulae for the distribution of singular values of a deterministic matrix multiplied by a truncated Haar orthogonal or symplectic matrix under conditions where the latter factor acts as a rank $1$ perturbation. Consequently, we generalize the recent Kieburg–Kuijlaars–Stivigny formula for the joint singular value density of a product of truncated unitary matrices to symplectic and orthogonal symmetry classes. Specializing to products of two symplectic matrices with a rank $1$ perturbative factor, we show that the squared singular values form a Pfaffian point process.

Titchmarsh–Weyl Formula for the Spectral Density of a Class of Jacobi Matrices in the Critical Case

We consider a class of Jacobi matrices with unbounded entries in the so-called critical (double root, Jordan block) case. We prove a formula which relates the spectral density of a matrix to the asymptotics of orthogonal polynomials associated with it.

Propagation of a Modified Complex Lorentz–Gaussian-Correlated Beam in a Marine Atmosphere

In this paper, we study the second-order statistics of a modified complex Lorentz–Gaussian-correlated (MCLGC) beam, which is a new type of partially coherent beam capable of producing an Airy-like intensity pattern in the far field, propagation through marine atmospheric turbulence. The propagation formula of spectral density is derived by the extended Huygens–Fresnel integral, which could explicitly indicate the interaction of turbulence on the beams’ spectral density under propagation. The influences of the structure constant of the turbulence, initial coherence width and wavelength on the spectral density are investigated in detail through numerical examples. In addition, analytical expressions for the r.m.s beam width, divergence angle and M2 factor of the MCLGC beam in the marine turbulence are also derived with the help of the Wigner distribution function. The results reveal that the beam spreads much faster, and the M2 factor deteriorates severely with the increase of the structure constant and the decrease of the inner scale size, whereas the outer scale size has little effect on these two quantities.