AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.

Adaptive coherence estimator based on the Krylov subspace technique for airborne radar

A novel adaptive detector for airborne radar space-time adaptive detection （STAD） in partially homogeneous environments is proposed. The novel detector combines the numerically stable Krylov subspace technique and diagonal loading technique, and it uses the framework of the adaptive coherence estimator （ACE）. It can effectively detect a target with low sample support. Compared with its natural competitors, the novel detector has higher proba- bility of detection （PD）, especially when the number of the training data is low. Moreover, it is shown to be practically constant false alarm rate （CFAR）.

EXPLICIT ERROR ESTIMATE FOR THE NONCONFORMING WILSON'S ELEMENT

In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.

Sharp estimates for Hübner’s upper bound function with applications

New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.

GRADIENT ESTIMATES FOR SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL

This note is a continuation of the work[17].We study the following quasilinear elliptic equations- △pu-μ/｜x｜p ｜u｜p-2 u=Q（x）｜u｜Np/N-p -2u,x∈R N,where 1 〈 p 〈 N,0 ≤ μ 〈（（N-p）/p）p and Q ∈ L∞（RN）.Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Hamilton-Souplet-Zhang's gradient estimates for two weighted nonlinear parabolic equations

In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.

On the Error Estimate of Adini's Element for the Second Order Problems

The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.

SOME INTEGRAL MEAN ESTIMATES FOR POLYNOMIALS

In this paper we establish L^q inequalities for polynomials, which in particular yields interesting generalizations of some Zygmund-type inequalities.

Estimated Green's function extracted from superconducting gravimeters and seismometers

Estimated Green’s function （EGF） between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical derivations assuming diffusive wave field, equi-partition of modes or random sources on an enclosed surface. This method provides a new approach to study the crust and mantle structure at regional scale, continental scale and global scale. Following the achievements with seismometer records, the records of infrasonic station, hydrophone and microphone were also used to obtain the EGFs of different wave fields. Since superconducting gravimeter is a better long period instrument than regular seismometer, EGF at longer period is expected to be obtained with the cross correlation of gravity data. In this paper, we will show the EGFs extracted by cross-correlations between the superconducting gravimeters and the seismometers. Both the travel times and dispersion curves obtained from different data types are consistent. The result shows that it is possible to retrieve the deep structure by the cross correlation of gravity data.

THE ERROR ESTIMATES OF HALLEY'S METHOD

In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.

GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS

The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.

Enhanced Wideband Frequency Estimation via FFT: Leveraging Polynomial Interpolation and Array Indexing

Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.

Anisotropic Interpolation Error Estimates of a Nonconforming Element

The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.

Stochastic Programming for Hub Energy Management Considering Uncertainty Using Two-Point Estimate Method and Optimization Algorithm

To maximize energy profit with the participation of electricity,natural gas,and district heating networks in the day-ahead market,stochastic scheduling of energy hubs taking into account the uncertainty of photovoltaic and wind resources,has been carried out.This has been done using a new meta-heuristic algorithm,improved artificial rabbits optimization(IARO).In this study,the uncertainty of solar and wind energy sources is modeled using Hang’s two-point estimating method(TPEM).The IARO algorithm is applied to calculate the best capacity of hub energy equipment,such as solar and wind renewable energy sources,combined heat and power(CHP)systems,steamboilers,energy storage,and electric cars in the day-aheadmarket.The standard ARO algorithmis developed to mimic the foraging behavior of rabbits,and in this work,the algorithm’s effectiveness in avoiding premature convergence is improved by using the dystudynamic inertia weight technique.The proposed IARO-based scheduling framework’s performance is evaluated against that of traditional ARO,particle swarm optimization(PSO),and salp swarm algorithm(SSA).The findings show that,in comparison to previous approaches,the suggested meta-heuristic scheduling framework based on the IARO has increased energy profit in day-ahead electricity,gas,and heating markets by satisfying the operational and energy hub limitations.Additionally,the results show that TPEM approach dependability consideration decreased hub energy’s profit by 8.995%as compared to deterministic planning.

Estimated Binding Energies of Drug-Like and Nondrug-Like Molecules in the Active Site of HIV-1 Integrase, 1BIS.pdb, and Two Mutant Models: Y143R and N155H

Lipinski’s “Rule of Five” was introduced for predicting oral bioavailability to describe drug-like molecules. For the purpose of this research the rules were used to separate potential inhibitors of HIV-1 integrase (1BIS.pdb) into two groups: drug-like and nondrug-like. If one of Lipinski’s “Rule of Five” was not followed the potential inhibitor was classified as nondrug-like. Thirty molecules were identified from the literature, twenty-four drug-like and six nondrug-like, that were docked into the active site of 1BIS.pdb (considered the non-mutated protein) and two mutant models, Y143R and N155H. These are two of the mutations that have led to increased resistance to HIV-1 integrase drugs such as raltegravir and elvitegravir. The computational software, ICM-Pro (Molsoft L.L.C.), was used to determine the estimated binding energy (EBE) of the drug/protein complex. It was found that the nondrug-like molecules generally had a more negative EBE, that is, tighter binding with 1BIS. pdb, though there were several exceptions in the drug-like group. With the protein mutant model Y143R, the majority of drug-like (58%) and nondrug-like molecules (67%) had tighter binding. However, for the mutant model N155H, there was the same percent (46%) of drug-like molecules with tighter binding with the mutant model as with 1BIS.pdb. The drug-like molecules were used when there was a ≥1 kcal/mole difference between 1BIS.pdb and either of the two mutant models to suggest a pharmacophore with structural characteristics for an HIV-1 integrase inhibitor.

ERROR ESTIMATES OF GALERKIN METHOD FOR HIGH DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.

Metallic Reserves of Submarine Manganese Nodules to be Estimated and Harnessed Prudently: Evidence from China's Jiaolong Manned Submersible

Since the discovery of oceanic manganese nodules during the expedition of the British ocean-going ship Challenger from 1872 to 1876, research and development for seabed manganese nodules have never ceased owing to the huge economic inducements. Manganese nodules are the black or dark brown, spherical or massive Mn-bearing ores, deposits of which are found on the sea bottom. The nodules are a mixture of silicate and insoluble potassium permanganates （also with sub-Ti, Fe and Na permanganates） that contain more than 30 kinds of metallic elements, among which those of greatest economic interest are Mn （27-30%）, Ni（1.25-1.5%）, Cu（1- 1.4%）, Co（0.2- 0.25 %）, Fe, Si, and AI, with minor amounts of Ca, Na, K, Ti, B, H and O.

C_(p,q)^(s+α)-forms Solution of _b-equ ation and Its L_(p,q)~s Estimates

In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.

The Estimates L_(1)-L_(∞) for the Reduced Radial Equation of Schrodinger

Estimates of the type L1-L∞ for the Schrödinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schrödinger Equation and are the essential elements in the study of the problems of initial values, the asymptotic times for large solutions and Scattering Theory for the Schrödinger equation and non-linear in general;for other equations of Non-linear Evolution. In general, the estimates Lp-Lp' express the dispersive nature of this equation. And its study plays an important role in problems of non-linear initial values;likewise, in the study of problems nonlinear initial values;see [1] [2] [3]. On the other hand, following a series of problems proposed by V. Marchenko [4], that we will name Marchenko’s formulation, and relate it to a generalized version of Theorem 1 given in [1], the main theorem (Theorem 1) of this article provides a transformation operator W?that transforms the Reduced Radial Schrödinger Equation (RRSE) (whose main characteristic is the addition a singular term of quadratic order to a regular potential V(x)) in the Schrödinger Equation on Half-Line (RSEHL) under W. That is to say;W?eliminates the singular term of quadratic order of potential V(x) in the asymptotic development towards zero and adds to the potential V(x) a bounded term and a term exponentially decrease fast enough in the asymptotic development towards infinity, which continues guaranteeing the uniqueness of the potential V(x) in the condition of the infinity boundary. Then the L1-L∞ estimates for the (RRSE) are preserved under the transformation operator , as in the case of (RSEHL) where they were established in [3]. Finally, as an open question, the possibility of extending the L1-L∞ estimates for the case (RSEHL), where added to the potential V(x) an analytical perturbation is mentioned.