A Possible Universal Model without Singularity and its Explanation for Evolution of the Universe

New hypotheses are proposed that there are s-particles and v-particles which are symmetric and mutually repulsive, there are S-space and V-space whose essential difference is only that their expectation values of the Higgs fields are different. In S-space the S-SU(5) symmetry is broken into S-SU(3)XU(1), and V-SU(5) symmetry still holds. As a consequence, s-particles get their masses determined by the SU(5) GUT and form the S-world, and v-particles are all massless and form SU(5) colour-single states which are identified with dark energy. The following results are obtained. There is no spacetime singularty, and there is the highest temperature in the universe. The creating process of one world is just the annihilating process of the other world in the highest temperature. A formula which well describes the luminous distance and redshift is obtained. The results of the Guth's inflationary scenario are obtained. Decelerated expanding early stage and accelerated expanding now stage of the universe are explained. New predictions are follows. Some huge cavities in V-space are not empty, in which there is s-matter with larger density, and are equivalent to huge concave lenses. The given tharacters of some huge cavities are well explained. The gravitation between two galaxies distant enough will lesser than that predicted by the conventional theory. A possible explanation for the big redshift of quasi-stellar objects is presented. Huge redshifts of quasars are mass redshifts. The universe is composed of infinite universal islands. It is possible that there is a new annihilating mode of black holes with their very huge masses, and there are very huge white holes which are different from that predicted by conventional theory.Comment: 36 pages, 2 figures, correct some mistakes, supplement some predicts, and correct the abstrct and reference [13

Quantum Field Theory Without Divergence A

On the basis a new conjecture, we present a new Lagrangian density and a new quantization method for QED, construct coupling operators and mass operators, derive scattering operators S_{f} and S_{w} which are dependent on each other and supplement new Feynman rules. S_{f} and S_{w} together determine a Fenman integral. Hence all Feynman integrals are convergent and it is unnecessary to introduce regularization and counterterms. That the energy of the vacuum state is equal to zero is naturally obtained. From this we can easily determine the cosmological constant according to data of astronomical observation, and it is possible to correct nonperturbational methods which depend on the energy of the ground state in quantum field theory. On the same basis as the new QED, we obtain naturally a new SU(2)XU(1) electroweak unified model whose L=L_{F}+L_{W} , here L is left-right symmetric. Thus the world is left-right symmetric in principle, but the part observed by us is asymmetric because L_{W} and L_{F} are all asymmetic. This model do not contain any unknown particle with a massive mass. A conjecture that there is repulsion or gravitation between the W-particles and the F-particles is presented. If the new interaction is gravitation, W-matter is the candidate for dark matter. If the new interaction is repulsion, W-matter is the origin of universe expansion.Comment: 52 pages, 12 figures. This is a more complete version with the following changes relative to the original. A. Supplement formulas (2.3.9a)-(2.3.9d) etc.; B. To correct some content

Distribution of Coefficients of Modular Forms and the Partition Function

Let $\ell\ge5$ be an odd prime and $j, s$ be positive integers. We study the distribution of the coefficients of integer and half-integral weight modular forms modulo odd positive integer $M$. As a consequence, we prove that for each integer $1\le r\le\ell^j$, $$\sharp\{1\le n\le X\ |\ p(n)\equiv r\pmod{\ell^j}\}\gg_{s,r,\ell^j}\frac{\sqrt X}{\log X}(\log\log X)^s.$$Comment: 8page

SU(5) Grand Unified Model and Dark Matter

A dark matter model which is called w-matter or mirror dark matter is concretely constructed based on (f-SU(5))X(w-SU(5)) symmetry. There is no Higgs field and all masses originate from interactions in the present model. W-matter is dark matter relatively to f-matter and vice versa. In high-energy processes or when temperature is very high, visible matter and dark matter can transform from one into another. In such process energy seems to be non-conservational, because dark matter cannot be detected. In low-energy processes or when temperature is low, there is only gravitation interaction of dark matter for visible matter.Comment: 7 pages, no figur

A Cosmological Model without Singularity and Dark Matter

According to the cosmological model without singularity, there are s-matter and v-matter which are symmetric and have oppose gravitational masses. In V-breaking s-matter is similar to dark energy to cause expansion of the universe with an acceleration now, and v-matter is composed of v-F-matter and v-W-matter which are symmetric and have the same gravitational masses and forms the world. The ratio of s-matter to v-matter is changeable. Based on the cosmological model, we confirm that big bang nucleosynthesis is not spoiled by that the average energy density of W-matter (mirror matter) is equal to that of F-matter (ordinary matter). According to the present model, there are three sorts of dark matter which are v-W-baryon matter (4/27), unknown v-F-matter (9.5/27) and v-W-matter (9.5/27). Given v-F-baryon matter (4/27) and v-W-baryon matter can cluster and respectively form the visible galaxies and dark galaxies. Unknown v-F-matter and v-W-matter cannot cluster to form any celestial body, loosely distribute in space, are equivalent to cold dark matter, and their compositions are unknown. The number in a bracket is the ratio of the density of a sort of matter to total density of v-matter. The decisive predict is that there are dark celestial bodies and dark galaxies. The energy of F-matter can transform into the energy of W-matter by such a process in which the reaction energy is high enough.Comment: 10 pages, 3 figure

Curvature estimates for the level set of spatial quasiconcave solutions to a class of parabolic equations

We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations u_t=F(\n^2u, \n u, u, t) under a structural condition, and give a geometric lower bound of the principal curvature of the spatial level surfaces.Comment: 22 page

The Maximal Matching Energy of Tricyclic Graphs

Gutman and Wagner proposed the concept of the matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let $G$ be a simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ be the roots of its matching polynomial. The matching energy of $G$ is defined to be the sum of the absolute values of $\mu_{i}\ (i=1,2,\ldots,n)$. Gutman and Cvetkoi\'c determined the tricyclic graphs on $n$ vertices with maximal number of matchings by a computer search for small values of $n$ and by an induction argument for the rest. Based on this result, in this paper, we characterize the graphs with the maximal value of matching energy among all tricyclic graphs, and completely determine the tricyclic graphs with the maximal matching energy. We prove our result by using Coulson-type integral formula of matching energy, which is similar as the method to comparing the energies of two quasi-order incomparable graphs.Comment: 16 pages, 4 figures, MATCH Communications in Mathematical and in Computer Chemistry, 201

A discrete computer network model with expanding dimensions

Complex networks with expanding dimensions are studied, where the networks may be directed and weighted, and network nodes are varying in discrete time in the sense that some new nodes may be added and some old nodes may be removed from time to time. A model of such networks in computer data transmission is discussed. Each node on the network has fixed dimensionality, while the dimension of the whole network is defined by the total number of nodes. Based on the spectacular properties of data transmission on computer networks, some new concepts of stable and unstable networks differing from the classical Lyapunov stability are defined. In particular, a special unstable network model, called devil network, is introduced and discussed. It is further found that a variety of structures and connection weights affects the network stability substantially. Several criteria on stability, instability, and devil network are established for a rather general class of networks, where some conditions are actually necessary and sufficient. Mathematically, this paper makes a first attempt to rigorously formulate a fundamental issue of modeling discrete linear time-varying systems with expanding dimensions and study their basic stability property.Comment: 14 pages, 0 figures, 6 referecne

Simulation of optical microfiber loop resonators for biochemical sensing

Based on the basic theory of the microfiber loop resonator, we exploit the application of microfiber loop resonators in biochemical sensing. We set up a reliable theoretical model and optimize the structural parameters of microfiber loop resonators including the radius of the microrfiber, the radius of the loop and the length of the coupling region for higher sensitivity, wider dynamic measurement range, and lower detection limit. To show the convincible and realizable sensing ability we perform the simulation of sensing an extreme small variation of ambient refractive index by employing a set of experimental datas as the parameters in the expression of intensity transmission coefficient, and the detection limit reaches to a varation of ambient refractive index of 10-5 refractive index unit(RIU). This has superiority over the exsiting evanescent field-based subwavelength-diameter optical fiber refractive index sensor.Comment: 8 pages,5 figure

Deep Mask For X-ray Based Heart Disease Classification

We build a deep learning model to detect and classify heart disease using $X-ray$. We collect data from several hospitals and public datasets. After preprocess we get 3026 images including disease type VSD, ASD, TOF and normal control. The main problem we have to solve is to enable the network to accurately learn the characteristics of the heart, to ensure the reliability of the network while increasing accuracy. By learning the doctor's diagnostic experience, labeling the image and using tools to extract masks of heart region, we train a U-net to generate a mask to give more attention. It forces the model to focus on the characteristics of the heart region and obtain more reliable results.Comment: outdated wor