SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

China:In the fourth quarter of 2023,exports of yarn and fabric to ASEAN ceased declining and rebounded

On January 8th,the China Chamber of Commerce for Import and Export of Textiles released data showing that in the fourth quarter,China’s textile and clothing exports gradually stabilised.The proportion of intermediate exports in textile and clothing exports continued to rise,providing a new impetus for the substantial expansion of exports to traditional markets and international supply chain cooperation.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Fenlong Cultivation-the Fourth Set of Farming Methods Invented in China

The basic theory and effect of the new farming method of ＂Fenlong＂ cultivation which has been included in the main extension technology of Ministry of Agriculture of the People＇s Republic of China is fully illustrated for the first time, and it is the fourth set （generation） of farming modes and methods following manpower, animal and mechanical （tractor） farming. It follows the natural law to achieve soil activation, water saving, oxygen increase, warming and desalination through the active use of natural resources like soil, rainfall and solar energy, thereby promoting a new round of natural agricultural production and quality improvement and water con- servation, which has crop yield increase by 10%-30%, quality improvement of 5%, natural precipitation retaining increase by100%. The characteristics and mechanism are the use of spiral drill for one-time completion of the land preparation by drilling vertically to 30-50 cm of soil layer through high speed peeling. After instant high temperature and many fierce impacts, mechanical frictions, it could achieve the multiplication of the number of loose soil, soil physical modification and expansion of the soil nutrients, reservoirs, oxygen, microorganisms （＂Four pools＂）. Fenlong cultivation can give birth to new farming culture and civilization, and it can achieve the physical ＂desalinized＂ transformation and utilization of saline soil. The formation of Fenlong green farming technology system makes it possible to invent the farming tools of ＂serf-propelled Fenlong machinery＂ that has got the patent, and it is the method for farmland （dry land, paddy field） Fenlong cultivation, saline-alkali soil smash-ridging cultivation and for the abundance of grass ecology on degraded grassland. The application of Fenlong ＂4＋1＂ （arable, saline-alkali soil, grasslands, Sponge City＋rivers） green development in China can achieve the ＂double safety＂ of food and living space.

ON STABILITY OF SOLUTIONS OF CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS

By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.

Stokes'first problem for the fourth order fluid in a porous half space

In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed.

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-（a＋bfR^3｜↓△u｜^2dx）△u＋V（x）u=f（x,u）,x∈R^3, u∈H^2（R3）,where a, b 〉 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti- Rabinowitz type condition.

Thermophoresis and concentration effects in a fourth grade peristaltic flow with convective walls

In this investigation,we have studied the peristaltic fluid flow in an asymmetric channel with convective walls.Fourth grade fluid model has been utilized in view of the fact that the results of all other differential type models can be deduced as the special case.Combined effects of heat and mass transfer are considered.The thermophoresis effects occur in the energy equation.Convective heat and mass boundary conditions have been given special attention.Long wave length and low Reynolds number approximations are utilized for the simplifications.Approximate analytic solutions for the velocity,temperature and concentration profiles are calculated using perturbation technique and elaborated in the form of graphical observations for various physical quantities.

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD

In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.

Effects of the fourth component and undercooling on morphology of primary Mg-Zn-Y icosahedral quasicrystal phase under normal casting conditions

The paper presents some results of the investigation on effects of the fourth component(Ti,C,Sb or Cu)and undercooling on the morphology,size and forming process of primary Mg-Zn-Y icosahedral quasicrystal phase(I-phase)under normal casting conditions.The result shows that the addition of certain amount of fourth component can transform I-phase morphology from petal-like to spherical.However,I-phase will grow up to petal-like if superfluous addition of the fourth component applied.It is also found that the solidified morphology of I-phase depends on the stability of spherical I-phase during the subsequent growth,and critical radius of maintaining the spherical I-phase interface relatively stable.Further,mini-sized spherical I-phase can be produced with high content of the fourth component by undercooling.Such findings are beneficial for industrializing Mgbased quasicrystals.

Comparison of Kurtosis and Fourth Power Detectors with Applications to IR-UWB OOK Systems

On-off keying (OOK) is one of the modulation schemes for non-coherent impulse radio Ultra-wideband systems. In this paper, the utilization of the kurtosis detector (KD) and fourth power detector (FD) receivers for OOK signaling is introduced. We investigate the effect of integration interval and the optimum threshold on the performance of energy detector (ED), KD and FD receivers. The semi analytic expression of BER is obtained by using generalized extreme value distribution function for KD and FD receivers. From performance point of view, the simulation results show that FD receiver outperforms KD and ED receivers. In contrast, the sensitivity to the optimum threshold is greatly reduced in KD receiver compared to ED and FD receivers.

Effective administration of cranial drilling therapy in the treatment of fourth degree temporal,facial and upper limb burns at high altitude:A case report

BACKGROUND Fourth degree burns damage the full thickness of the skin and affect underlying tissues.Skin grafting after debridement is often used to cover the wounds of salvageable severe burns.A granulation wound can be formed by drilling the skull to the barrier layer to solve the problem of skull exposure.Low oxygen levels present at high altitudes aggravate ischemia and hypoxia which can negatively impact wound healing.The impaired healing in such cases can be ameliorated by hyperbaric oxygen therapy.CASE SUMMARY We describe a patient who presented with fourth degree burns to the left temporal and facial regions upon admission in December 2018.The periosteum of the skull and the deep fascia of the face were exposed.After the first stage of debridement and skin grafting,the temporal skin did not survive well.Granulation was induced by cranial drilling,and then a local flap was transferred to cover the wound.The left temporal and facial wounds were completely covered and the patient recovered well.CONCLUSION Skin grafting and flap transfer after early debridement to cover the wound and control infection were of great significance.In the later stages of the patient's treatment,survival of the skin graft and skin flap was observed.The second stage repair was performed to achieve successful skin grafting by cranial granulation.Granulation was formed by drilling the skull,and then the wound was closed,which is suitable for cases with skull exposure and wounds with poor blood supply.We consider that hyperbaric oxygen treatment and improving tissue oxygen supply were beneficial in this patient.

Hybrid Effects of Thermal and Concentration Convection on Peristaltic Flow of Fourth Grade Nanofluids in an Inclined Tapered Channel: Applications of Double-Diffusivity

This article brings into focus the hybrid effects of thermal and concentration convection on peristaltic pumping of fourth grade nanofluids in an inclined tapered channel.First,the brief mathematical modelling of the fourth grade nanofluids is provided along with thermal and concentration convection.The Lubrication method is used to simplify the partial differential equations which are tremendously nonlinear.Further,analytical technique is applied to solve the differential equations that are strongly nonlinear in nature,and exact solutions of temperature,volume fraction of nanoparticles,and concentration are studied.Numerical and graphical findings manifest the influence of various physical flow-quantity parameters.It is observed that the nanoparticle fraction decreases because of the increasing values of Brownian motion parameter and Dufour parameter,whereas the behaviour of nanoparticle fraction is quite opposite for thermophoresis parameter.It is also noted that the temperature profile decreases with increasing Brownian motion parameter values and rises with Dufour parameter values.Moreover,the concentration profile ascends with increasing thermophoresis parameter and Soret parameter values.

Fourth Industrial Revolution:Technological Drivers,Impacts and Coping Methods

The world is marching into a new development period when the digital technology,physical technology,and biological technology have achieved an unprecedented development respectively in their own fields,and at the same time their applications are converging greatly.These are the three major technological drivers for the Fourth Industrial Revolution.This paper discusses the specific technology niches of each kind technological driver behind the Fourth Industrial Revolution,and then evaluates impacts of the Fourth Industrial Revolution on global industrial,economic,and social development.At last this paper proposes possible measures and policies for both firms and governments to cope with the changes brought by the Fourth Industrial Revolution.

Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part III. An Original Solution of Hilbert’s Fourth Problem

This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.

May Fourth Movement in China-language Planning and Innovation

The purpose of this paper is to establish a clear comprehension and discernment of fundamental concepts of the languageplanning field and its correlation with and differences from innovation and change.It focuses on five aspects:a new language policyadopted in the period of late Qing;the status of classic Chinese in ancient times and the new vernacular in modern Chinese;the ori-gins of new vernacular;the problem that appeared alongside the new vernacularand the influence of May Fourth Movement in soci-ety and in education area.

The Energy-orthogonal Tetrahedral Finite Element for Fourth Order Elliptic Equations

In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions.The newly constructed element is proved to be convergent for a model biharmonic equation.

Turiyam Set a Fourth Dimension Data Representation

Recently most of the authors focused on dealing with uncertainty. To deal with that algebra of fuzzy sets is introduced in three-way fuzzy space. It gave way to characterize the attributes in true, false or uncertain regions. It is found in chemistry also as an electron, proton and neutron. The problem arises when the attributes are beyond the three-dimensions. One of suitable examples is winning, draw or loss of a match cannot define the win draw or loss of series. It is measured in international relationships also like USA-China, USA-Russia, India-Pakistan or Israel-Philistine. Some countries support the USA, some countries support China, some countries are neutral in hidden consciousness to fulfill their agenda. It is also measured in democratic countries like India where some people vote in favor of a party, some people vote against the given party, some people may be absent or walkout whereas some people vote NOTA. This last dimension is called as Turiyam or fourth dimension. This last dimension is influenced from Yin-Yang theory of Chinese Taoism as well as Sanskrit Yamma-Yammi and its complement. The Turiya means measuring each dimension in silent mode. There is less attention paid towards the necessity of fourth dimensions and its algebra. This paper will discuss gimbal lock of three-way fuzzy space using the Tuiyam set and its algebra.