Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

An Empirical Study on Rural Economic Growth in Hubei Province Based on New C-D Production Function

Human capital is becoming a major driving force of promoting economic growth and social development. Hubei Province as a large agricultural province is significantly affected by the human capital. The paper selects the correlation data about rural economic growth in Hubei Province as samples to analyze the contribution of physical capital and human capital to rural economic growth by the new C-D function and SPSS22. 0. The results show that the effect of the elasticity of human capital is greater than that of physical capital in rural economic development; the high quality rural human capital storage and the average years of schooling of rural labor force will increase the net income of rural household. Therefore,we should not only increase input of physical capital but also increase the input of human capital to raise the level of human capital in rural areas and promote sustainable development of rural economy.

A new kind of special function and its application

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.

A New Research about Pion Parton Distribution Function

A new fit of the pion parton distribution functions is provided. Only valence quark distributions are used at a low evolution scale and are evolved with the modified Dokshitzer- Gribov-Lipatov-Altarelli-Parisi equation which is briefly introduced in this work, and the sea quark and gluon distributions are only generated by the quantum chromodynamics processes. We find that the patton distributions can explain the pion-nucleon experiments data well, and it can also be compared with the data from the leading neutron data of experiments at HERA. The momentum distributions among the partons are discussed and our results are consistent with some models.

Analysis on Function Orientation and Development Countermeasures of New Agricultural Business Entities

Along with the rapid advance of industrialization and urbanization process, fostering new agricultural business entities become inevitable for agricultural transformation and the construction of agricultural modernization in China. The status of the new agricultural business entities determines the level of modern agricultural development. In recent years, new agricultural business entities have grew rapidly. However, there are still many problems including the difficulties in financing loans, inadequate agricultural insurance system, bad implementation of agricultural subsidies, jagged agricultural talents and so on. In order to foster new agricultural business entities, countermeasures should be carried out to ensure financial support, perfect the agricultural insurance, strengthen the level of agricultural subsidies, strive to develop the degree of specialization agricultural operators and so on.

New useful special function in quantum optics theory

By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators（IWOP） we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.

New insights into the functions of Ptd Ins(3,5)P_2 in the pathogenisis of neurodegenerative disorders

The membrane trafficking systems in brain play an important role in the regulation of neuronal processes,such as morphology,neuronal survival and synaptic plasticity.It has been suggested that the phosphatidylinositols（PIs）located on endolysosomal membranes play a key role in controlling this trafficking systems.

Chairman Yu Zhen on New Functions of China National Council of Light Industry

The China National Council of Light Industry is the reshuffled former Ministry of Light Industry. It began operation in Beijing on July 15, 1993. Chairman Yu Zhen gave the following introduction on the council’s work: The China National Council of Light Industry retains the administration functions and responsibilities of the former Ministry of Light Industry. Its functions of coordination, service

Do new neurons contribute to functional reorganization after brain damage?

The finding that adult neurogenesis occurs constitutively in the brain was a breakthrough in neuroscience and soon gained attention as a possible mechanism for neurorepair after brain damage. In a recent study we show that the dentate gyrus （DG） reorganizes anatomically over neurons undergo maturation time after damage, while new and activate in response to a contextual fear memory recall （Aguilar-Arredondo and Zepeda, 2018）. These findings provide new evidence on the possible role of neurogenesis in cognitive recovery after brain injury.

SLP-2: a potential new target for improving mitochondrial function in Parkinson's disease

Parkinson＇s disease （PD） is a progressive neurodegenerative disease, which is generally considered a multifactorial disorder that arises owing to a combination of genes and environmental factors. While most cases are idiopathic, in about 10% of the patients a genetic cause can be detected, ascribable to mutations in more than a dozen genes. PD is characterized clinically by tremor, rigidity, reduced mo- tor activity （bradykinesia）, and postural instability and pathological- ly by loss of dopaminergic （DA） neurons in the substantia nigra pars compacta, loss of DA innervation in the striatum, and the presence of a-synuclein positive aggregates in the form of Lewy bodies. The symptomatic treatment of PD with levodopa, which aims at replac- ing dopamine, remains the gold standard, and no neuroprotective or disease-modifying therapy is available. During treatment, the disease continues to progress, and long-term use of levodopa has import- ant limitations including motor complications termed dyskinesias. Therefore, a pharmacological therapy able to prevent or halt the neu- rodegenerative process is urgently required.

The Separation of Powers from Functions and the Establishment of a New Structure of Management and Operation of State-owned Assets

The development of the socialist market economy demands the furtherintensification of the reform of the management operating system (MOS)of the state-owned assets, the strengthening of the efficiency in the man-agement of state-owned assets,and the improvement of the operating bene-

A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS

In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].

Functional food products in Japan:A review

Japan has a long history of using foods with health benefits and Japanese people are well-known for their longevity.In 1991,the Ministry of Health,Labor and Welfare introduced a functional food regulation called“foods for specified health uses”(FOSHU)in Japan.After the introduction of the functional food system,many clinically proven FOSHU products with health benefits have been developed and launched in the market.As a result,the net sales of FOSHU products reached 6.2 billion dollars in 2007.Most of the health claims relate to improving gastro-intestinal health using probiotics.Triglycerides,high blood pressure,high LDL-cholesterol,and high blood glucose are mainly associated with the related health claims.After 2007,the market for FOSHU products was almost saturated.However,a novel functional regulatory system\called“Foods with Function Claims”was established in 2015 based on the Dietary Supplement Health and Education Act system established in the USA.Major health claims in the new regulation system are associated with fatigue,eyes,memory,stress,sleep,joints,blood flow,body temperature,muscles,and Body Mass Index.After the introduction of the new system,the total sales for functional foods including FOSHU products reached 8 billion dollars in 2018.The new functional regulatory system is more flexible in terms of health claims,the protocol for clinical studies,and the required results.Therefore,the market for new regulatory products is still growing.In the present paper,the potential of both regulatory systems and some related issues will be discussed.

Higher Order Solitary Wave Solutions of the Standard KdV Equations

Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and the Species of Polymers

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

New functions of VCSEL-based optical devices Invited Paper

We have seen a lot of unique features off vertical cavity surface emitting lasers （VCSELs）, such as low power consumption, wafer-level testing, small packaging capability, and so on. The market of VCSELs has been growing up rapidly in recent years and they are now the key devices in local area networks using multi-mode optical fibers. In addition, new functions on VCSELs have been demonstrated. In this paper, the recent advances of VCSEL photonics will be reviewed which include the wavelength engineering and the athermal operation based on microelectro mechanical system （MEMS） technologies. Also, this paper explores the potential and challenges for new functions of VCSELs, including high-speed control of optical phase, slow light devices, plasmonic VCSELs, and so on.

Learning to memorize: shedding new light on prefrontal functions

Working memory is one of the essential higher cognitive functions that actively holds behaviorally-relevant information essential for guiding subsequent actions. It includes subsystems that store and manipulate singlemode or multi-modal sensory information, e.g., spatial information, visual images, auditory scenes, olfactory objects, or any combination of these. In addition to merely holding a certain amount of information for a short period of time, as is generally believed, the cognitive processes involved are far more complex, including the executive and attentional control of short-term memory, permitting interim integration, and the processing, disposal, and retrieval of information. Evolution-wise, working memory is essential for the behavioral flexibility that allows humans and animals to quickly adapt to rapidly changing environments.

A New Jacobi Elliptic Function Expansion Method for Solving a Nonlinear PDE Describing Pulse Narrowing Nonlinear Transmission Lines

In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations （PDEs） based on the ho- mogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff＇s current law and Kirchhoff＇s voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation （ODE） using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained.

New function of an old molecule——VCAM1 guides neural stem cells from proliferation to quiescence

Subject Code:C12With the support by the National Natural Science Foundation of China,the group led by Prof.Shen Qin(沈沁)from the Center for Stem Cell Biology and Regenerative Medicine,School of Medicine,and the IDG/McGovern Institute for Brain Research at Tsinghua University,reported a newly discovered

A new zeta function for number fields

According to the idea of class field theory, the possible absolutely normal number fieldsare restricted in nature by the arithmetical properties of rational number field .Becausethe fundamental arithmetical property of is the distributive law of the prime numbers,