A Method to Reduce the Lehmer Measure in a Multi-Term Machin-Like Formula for π

Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for π. As a further development, here we show how to generate a multi-term Machin-like formula for π with a reduced Lehmer measure. The Mathematica codes validating these results are presented.

Influencing factors and preventive measures of infectious complications after intestinal resection for Crohn’s disease

The incidence of Crohn’s disease(CD)has increased in recent years,with most patients requiring intestinal resection.Complications after intestinal resection for CD can lead to poor prognosis and recurrence,among which infectious complic-ations are the most common.This study aimed to investigate the common risk factors,including medications,preoperative nutritional status,surgery-related factors,microorganisms,lesion location and type,and so forth,causing infectious complications after intestinal resection for CD,and to propose corresponding preventive measures.The findings provided guidance for identifying suscept-ibility factors and the early intervention and prevention of infectious complic-ations after intestinal resection for CD in clinical practice.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

Tracking a maneuvering target in clutter with out-of-sequence measurements for airborne radar

There are many proposed optimal or suboptimal al- gorithms to update out-of-sequence measurement（s） （OoSM（s）） for linear-Gaussian systems, but few algorithms are dedicated to track a maneuvering target in clutter by using OoSMs. In order to address the nonlinear OoSMs obtained by the airborne radar located on a moving platform from a maneuvering target in clut- ter, an interacting multiple model probabilistic data association （IMMPDA） algorithm with the OoSM is developed. To be practical, the algorithm is based on the Earth-centered Earth-fixed （ECEF） coordinate system where it considers the effect of the platform＇s attitude and the curvature of the Earth. The proposed method is validated through the Monte Carlo test compared with the perfor- mance of the standard IMMPDA algorithm ignoring the OoSM, and the conclusions show that using the OoSM can improve the track- ing performance, and the shorter the lag step is, the greater degree the performance is improved, but when the lag step is large, the performance is not improved any more by using the OoSM, which can provide some references for engineering application.

Confirmatory factor analysis of VISA-P scale and measurement invariance across sexes in athletes with patellar tendinopathy

Background:The Victorian Institute of Sport Assessment–Patella(VISA-P) scale is the most condition-specific patient-reported outcome measure used to assess symptom severity in athletes with patellar tendinopathy.Previous exploratory factor analyses have been conducted to evaluate the scale's dimensionality,with inconsistent results,and the factor structure of the scale remains unclear.The aims of the present study were to determine the factorial structure of the VISA-P scale using confirmatory factor analysis(CFA) and test measurement invariance across sexes.Methods:The study included a convenience sample of 249 Spanish athletes with patellar tendinopathy.CFA was performed to assess factorial validity.Hypothesized 1-and 2-factor models were tested.Measurement invariance across sexes was evaluated via multi-group CFA with several fit indices using EQS 6.1 software.Results:The internal consistency coefficient was 0.74.Several CFA models were examined and the 1-factor model in which errors for Items 7 and8 were correlated showed acceptable fit in terms of comparative fit index(CFI) and goodness-of-fit index(GFI) statistics(CFI = 0.93;GFI = 0.94;standardized root mean square residual = 0.06;root mean square error of approximation = 0.10;90% confidence interval:0.08–0.13).This model was invariant across sexes.Conclusion:The 1-factor model of the Spanish version of the VISA-P scale(VISA-P-Sp) in which errors for Items 7 and 8 were correlated demonstrated relative fit in CFA.Scores obtained via VISA-P-Sp can be compared between men and women without sexes bias.Further studies should examine the VISA-P scale and other single-score patient-reported outcome measures concurrently.

Resilience based importance measure analysis for SoS

In a system of systems(SoS),resilience is an important factor in maintaining the functionality,stability,and enhancing the operation effectiveness.From the perspective of resilience,this paper studies the importance of the SoS,and a resilience-based importance measure analysis is conducted to provide suggestions in the design and optimization of the structure of the SoS.In this paper,the components of the SoS are simplified as four kinds of network nodes:sensor,decision point,influencer,and target.In this networked SoS,the number of operation loops is used as the performance indicator,and an approximate algorithm,which is based on eigenvalue of the adjacency matrix,is proposed to calculate the number of operation loops.In order to understand the performance change of the SoS during the attack and defense process in the operations,an integral resilience model is proposed to depict the resilience of the SoS.From different perspectives of enhancing the resilience,different measures,parameters and the corresponding algorithms for the resilience importance of components are proposed.Finally,a case study on an SoS is conducted to verify the validity of the network modelling and the resiliencebased importance analysis method.

Integrability near the Boundary of the Poisson Integral of Some Singular Measures

We consider the Poisson integral u = P＊μ on the half-space R＋^N＋1 （ N 〉 1 ） （or on the unit ball of the complex plane） of some singular measureμ. If μ is an s-measure （0 〈 s 〈 N）, then some sharp estimates of the integration of the harmonic function u near the boundary are given. In particular, we show that fpr p〉1,∫R^Nu^p（x,y）dx- y^-τ （y〉0,τ =（N-s）（p-1） ） （Given for p〉1, RN f 〉 0 and g 〉 0, ＂ f-g ＂ will mean that there exist constants C1 and C2, such that C1f ≤ g ≤ CEf ）.

Supplier Evaluation Model Based on Fuzzy Measures and Choquet Integral

To identify interactions among evaluation criteria and describe their importance,a new identification method making use of a fuzzy measure is presented.The relative weight and interaction degree of every evaluation criteria pair are obtained by using the diamond pairwise comparison method.Based on comparison results,the maximum eigenvector method of analytic hierarchy process （AHP）,the hierarchical clustering method,and the phi（s） transformation are utilized to generate values of the fuzzy measure for each subset of the evaluation criterion set.Overall evaluation on each supplier is aggregated by Choquet integral with respect to the fuzzy measure.Finally,an illustrative example demonstrates the practical feasibility and validity of the proposed method.

Simultaneous measurements of aeroacoustic sounds and wall vibration for exploring the contribution of tooth vibration in the production of sibilant sounds/s/

In order to understand the contribution of teeth vibration to the production of sibilant/s/, the pre-sent study was designed to develop a method of simultaneously measuring aeroacoustic sounds and the vibration of an obstacle. To measure the vibration without disturbing flow, the Michelson interferometer was employed. The flow channel, which had an obstacle wall inside of it, was fabricated such that it morphologically mimicked the simplified geometry of the oral cavity. Given airflows at a flow rate of 7.5 × 10–4 m3/s from the inlet, aeroacoustic sounds were generated. A spectrum analy-sis of the data demonstrated two prominent peaks in the sound at 1,300 and 3,500 Hz and one peak in the wall vibration at 3,500 Hz. The correlation in peak frequencies between the sound and wall vibration suggests that the sound at 3,500 Hz was induced by the wall vibration. In fact, the sound amplitude at 3,500 Hz decreased when the obstacle wall was thickened, which increased its rigidity (p < 0.05, t-test). The experimental results demonstrate that the developed techniques are capable of measuring aeroacoustic sound and obstacle wall vibration simultaneously, and suggest the potential to pave the way for detailed analysis of the production of sibilant sounds /s/.

Nikodým-Type Theorems for Lattice Group-Valued Measures with Respect to Filter Convergence

We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.

The matrix representation for the mathematic structure of Shannon’s information measures

Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.

Precision Frequency Measurement of ^(87)Rb 5S_(1/2)(F=2)→5D_(5/2)(F″=4)Two-Photon Transition through a Fiber-Based Optical Frequency Comb

The absolute frequency of 87Rb 5S1/2 （F=2）→5D5/2 （F＂ = 4） two-photon transition at 778nm is measured in an accuracy of 44kHz. A home-made erbium-doped fiber laser frequency comb with frequency stability of 5.0 × 10-13@1 s is employed for the light source. By using a periodically poled lithium niobate, the femtosecond pulse operating in 1556 nm is frequency-doubled to 778 nm to obtain the direct two-photon transition spectroscopy of thermal rubidium vapor. Through sweeping the carrier envelope offset frequency （fceo）, the 5S1/2 （F=2）→5D5/2 （F＂ = 4） two-photon transition line is clearly resolved and its absolute frequency is determined via the peak-finding of the fitting curve. After the frequency correction, the measured result agrees well with the previous experiment on this transition. The entire potential candidate of optical frequency standard for system configuration is compact and robust, providing a telecommunication applications.

Novel similarity measures for face representation based on local binary pattern

The successful face recognition based on local binary pattern(LBP)relies on the effective extraction of LBP features and the inferring of similarity between the extracted features.In this paper,we focus on the latter and propose two novel similarity measures for the local matching methods and the holistic matching methods respectively.One is Earth Mover's Distance with Hamming and Lp ground distance(EMD-HammingLp),which is a cross-bin dissimilarity measure for LBP histograms.The other is IMage Hamming Distance(IMHD),which is a dissimilarity measure for the whole LBP images.Experiments on FERET database show that the proposed two similarity measures outperform the state-of-the-art Chi-square similarity measure for extraction of LBP features.

Von Neumann’s Theory, Projective Measurement, and Quantum Computation

We discuss the fact that there is a crucial contradiction within Von Neumann’s theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1 ≤ N to a new constant . It may be said that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does. We discuss how our solution is used in an implementation of Deutsch’s algorithm.

The diagnostic value of liver stiffness measurement combined with S index in the degree of hepatitis B liver fibrosis

Objective:To investigate the value of liver stiffness measurement(LSM)combined with S index in predicting the degree of liver fibrosis in hepatitis B patients.Methods:A total of 187 chronic hepatitis B patients who were admitted to the Department of Infection,the First Affiliated Hospital of Hainan Medical College from January 2019 to December 2021 were selected.General data were collected,blood routine,liver function,liver fibrosis and liver stiffness measurement were tested,and S index,APRI and FIB-4 index were calculated,and liver biopsy was performed.Results:According to the pathological results of liver puncture,The patients were divided into no significant fibrosis group(n=86),significant fibrosis group(n=71)and cirrhosis group(n=30).There were significant differences in age,PLT,GGT,ALB,S index,HA,LN and LSM levels among the three groups(P<0.05).There was a good correlation between S index and the degree of hepatic fibrosis(rs=0.738,P<0.001).The AUC of S index and LSM for the diagnosis of significant fibrosis in hepatitis B were 0.873 and 0.792,respectively.And the AUC of S index and LSM for the diagnosis of liver cirrhosis were 0.966 and 0.879,respectively.The AUC for the combined diagnosis of significant fibrosis and cirrhosis were 0.908 and 0.988,respectively.The AUROC of combined detection in the diagnosis of cirrhosis was higher than that of LSM,APRI and FIB-4(P<0.05).Conclusion:LSM combined with S index has certain application value in the diagnosis of liver fibrosis/cirrhosis in hepatitis B patients.

Schrödinger’s Cat Paradox Resolution Using GRW Collapse Model: Von Neumann Measurement Postulate Revisited

In his famous thought experiment, Schr?dinger (1935) imagined a cat that measures the value of a quantum mechanical observable with its life. Since Schr?dinger’s time, no any interpretations or modifications of quantum mechanics have been proposed which give clear unambiguous answers to the questions posed by Schr?dinger’s cat of how long superpositions last and when (or whether) they collapse? In this paper appropriate modification of quantum mechanics is proposed. We claim that canonical interpretation of the wave function is correct only when the supports of the wave functions and essentially overlap. When the wave functions and have separated supports (as in the case of the experiment that we are considering in this paper) we claim that canonical interpretation of the wave function is no longer valid for a such cat state. Possible solution of the Schr?dinger’s cat paradox is considered. We pointed out that the collapsed state of the cat always shows definite and predictable outcomes even if cat also consists of a superposition: .

Convergence of Impact Measures and Impact Bundles

Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that pointwise convergence is maintained by all well-known impact bundles(such as the h-,g-,and R-bundle)and that theμ-bundle even maintains uniform convergence.Based on these results,a classification of impact bundles is given.Research limitations:As for all impact studies,it is just impossible to study all measures in depth.Practical implications:It is proposed to include convergence properties in the study of impact measures.Originality/value:This article is the first to present a bundle classification based on convergence properties of impact bundles.

Rough law energy and measurement of ■-decomposition rough law

By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.

Combined soft measurement on key indicator parameters of new competitive advantages for China’s export

The estimation of the difference between the new competitive advantages of China’s export and the world’s trading powers have been the key measurement problems in China-related studies.In this work,a comprehensive evaluation index system for new export competitive advantages is developed,a soft-sensing model for China’s new export competitive advantages based on the fuzzy entropy weight analytic hierarchy process is established,and the soft-sensing values of key indexes are derived.The obtained evaluation values of the main measurement index are used as the input variable of the fuzzy least squares support vector machine,and a soft-sensing model of the key index parameters of the new export competitive advantages of China based on the combined soft-sensing model of the fuzzy least squares support vector machine is established.The soft-sensing results of the new export competitive advantage index of China show that the soft measurement model developed herein is of high precision compared with other models,and the technical and brand competitiveness indicators of export products have more significant contributions to the new competitive advantages of China’s export,while the service competitiveness indicator of export products has the least contribution to new competitive advantages of China’s export.

Quantum Inverse Measurement Theory Contributing to the Birth of Interpretation System of Quantum Mechanics of Local-Realism and Determinism

The existing interpretation of quantum mechanics is contrary to common sense. The existing quantum mechanical interpretation schemes are puzzling. The confusing theory is unconvincing, and needs to be amended and completed. The successful interpretation program of quantum mechanics of local-realism and determinism is undoubtedly the most attractive. Preparing the interpretation program deserves to be chosen as a research goal. It is a very good premise to believe that an object particle consists of light-knot of monochromatic waves. According to this premise, the erroneous recognition about “superposition principle, wave-particle duality and uncertainty principle” can be corrected. Under this premise, above research goal is achieved by establishing, applying quantum mechanics inverse measurement theory, adhering to the principle that there must be a complete empirical chain in the derivation process of experimental conclusion, and using the side effect caused by accompanying-light to explain the diffraction experiment of object particles. Electron secondarily diffraction and other experiments directly prove that there is the measurement (observation) which may not destroy quantum coherence. The diffraction experiments of all kinds of particles show that the Keeping and playing of the coherence of moving particles in the vacuum have nothing to do with their previous experience. These are the existing experiments, to be found, that support the theory of quantum inverse measurements. The verification experiment of quantum inverse measurement is designed. The absolute superiorities of quantum inverse measurement and the new view of measurement of quantum mechanics are listed. These superiorities are that: it has the characteristics of local-realism and determinism;it is not contrary to common sense and there is no confusing place;it can predict several phenomena that cannot be predicted by other theories. A solid theoretical foundation has been laid for “correctly understanding the microscopic world” and establishment of local realism quantum mechanics.