Modified Wave Particle Duality and Black Hole Physics

de Broglie relation is revisited, in consideration of a generalization of canonical commuting relation. The possible effects on particle's localization and black hole physics are also discussed, in a heuristic manner.     

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows.     

KEADA: Identifying Key Classes in Software Systems Using Dynamic Analysis and Entropy-Based Metrics

Software maintenance is indispensable in the software development process. Developers need to spend a lot of time and energy to understand the software when maintaining the software, which increases the difficulty of software maintenance. It is a feasible method to understand the software through the key classes of the software. Identifying the key classes of the software can help developers understand the software more quickly. Existing techniques on key class identification mainly use static analysis techniques to extract software structure information. Such structure information may contain redundant relationships that may not exist when the software runs and ignores the actual interaction times between classes. In this paper, we propose an approach based on dynamic analysis and entropy-based metrics to identify key classes in the Java GUI software system, called KEADA (identifying KEy clAsses based on Dynamic Analysis and entropy-based metrics). First, KEADA extracts software structure information by recording the calling relationship between classes during the software running process; such structure information takes into account the actual interaction of classes. Second, KEADA represents the structure information as a weighted directed network and further calculates the importance of each node using an entropy-based metric OSE (One-order Structural Entropy). Third, KEADA ranks classes in descending order according to their OSE values and selects a small number of classes as the key class candidates. In order to verify the effectiveness of our approach, we conducted experiments on three Java GUI software systems and compared them with seven state-of-the-art approaches. We used the Friedman test to evaluate all approaches, and the results demonstrate that our approach performs best in all software systems.     

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Amp`ere law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.     

Structural Characteristics,Antioxidant and Hypoglycemic Activities of Polysaccharide from Siraitia grosvenorii

The structural characterization, the in vitro antioxidant activity, and the hypoglycemic activity of a polysaccharide (SGP-1-1) isolated from Siraitia grosvenorii (SG) were studied in this paper. SGP-1-1, whose molecular weight is 19.037 kDa, consisted of Gal:Man:Glc in the molar ratio of 1:2.56:4.90. According to the results of methylation analysis, GC–MS, and NMR, HSQC was interpreted as a glucomannan with a backbone composed of 4)-β-D-Glcp-(1→4)-, α-D-Glcp-(1→4)-, and 4)-Manp-(1 residues. α-1,6 linked an α-D-Galp branch, and α-1,6 linked an α-D-Glcp branch. The study indirectly showed that SGP-1-1 has good in vitro hypoglycemic and antioxidant activities and that these activities may be related to the fact that the SGP-1-1’s monosaccharide composition (a higher proportion of Gal and Man) is the glycosidic-bond type (α- and β-glycosidic bonds). SGP-1-1 could be used as a potential antioxidant and hypoglycemic candidate for functional and nutritional food applications.     

一类利用回归关系的计量指标抽样方案

在产品质量判定的抽样检验问题中,当目标指标需用破坏性试验才能得其值时,更为常用的是用非破坏性试验可得量值的协变指标量来预报它。但在产品抽样验收问题上,未能形成理论较为严密的方法,这是由于预报误差这个关键问题的处理尚未解决得好,即给不出抽样方案的功效计算的正确或是近似性较好的公式。本文通过建立合理的数学模型,把对目标指标的质量要求化为对协变指标量的统计要求,从而利用两者的回归关系,结合两种复杂的抽样方案,给出功效函数的计算公式和计算方法,并进行了分析。     

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.     

Multiple Jacobi Elliptic Function Solutions to Integrable Higher Order Broer-Kaup Equation in (2+1)-Dimensional Spaces

In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained.     

Anticonvulsant Effect of Turmeric and Resveratrol in Lithium/Pilocarpine-Induced Status Epilepticus in Wistar Rats

Epilepsy is a chronic neurological disorder that lacks a cure. The use of plant-derived antioxidant molecules such as those contained in turmeric powder and resveratrol may produce short-term anticonvulsant effects. A total of 42 three-month-old male Wistar rats were divided into six groups (n = 7 in each group): Vehicle (purified water), turmeric (150 and 300 mg/kg, respectively), and resveratrol (30 and 60 mg/kg, respectively), administered per os (p.o.) every 24 h for 35 days. Carbamazepine (300 mg/kg/5 days) was used as a pharmacological control for anticonvulsant activity. At the end of the treatment, status epilepticus was induced using the lithium–pilocarpine model [3 mEq/kg, intraperitoneally (i.p.) and 30 mg/kg subcutaneously (s.c.), respectively]. Seizures were evaluated using the Racine scale. The 300 mg/kg of turmeric and 60 mg/kg of resveratrol groups had an increased latency to the first generalized seizure. The groups treated with 150 and 300 mg/kg of turmeric and 60 mg/kg of resveratrol also had an increased latency to status epilepticus and a decreased number of generalized seizures compared to the vehicle group. The chronic administration of turmeric and resveratrol exerts anticonvulsant effects without producing kidney or liver damage. This suggests that both of these natural products of plant origin could work as adjuvants in the treatment of epilepsy.     

Age Analysis of Status Updating System with Probabilistic Packet Preemption

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.