On the Dimension and Euler characteristic of random graphs

The inductive dimension dim(G) of a finite undirected graph G=(V,E) is a rational number defined inductively as 1 plus the arithmetic mean of the dimensions of the unit spheres dim(S(x)) at vertices x primed by the requirement that the empty graph has dimension -1. We look at the distribution of the random variable "dim" on the Erdos-Renyi probability space G(n,p), where each of the n(n-1)/2 edges appears independently with probability p. We show here that the average dimension E[dim] is a computable polynomial of degree n(n-1)/2 in p. The explicit formulas allow experimentally to explore limiting laws for the dimension of large graphs. We also study the expectation E[X] of the Euler characteristic X, considered as a random variable on G(n,p). We look experimentally at the statistics of curvature K(v) and local dimension dim(v) = 1+dim(S(v)) which satisfy the Gauss-Bonnet formula X(G) = sum K(v) and by definition dim(G) = sum dim(v)/|V|. We also look at the signature functions f(p)=E[dim], g(p)=E[X] and matrix values functions A(p) = Cov[{dim(v),dim(w)], B(p) = Cov[K(v),K(w)] on the probability space G(p) of all subgraphs of a host graph G=(V,E) with the same vertex set V, where each edge is turned on with probability p. If G is the complete graph or a union of cyclic graphs with have explicit formulas for the signature polynomials f and g.Comment: 18 pages, 14 figures, 4 table

Creative Fusion: Dim Sum Variation for Vegetarians Using White Tofu with Carrots, Bamboo Sprouts, and Mushroom Substitute

Dim sum typically contains items derived from animals, and the main ingredients in this vegetarian Dim sum are carrot white tofu, white tofu mushroom, and white tofu bamboo sprout, which the author makes without animal products. The aim of this study was to determine how well the vegetarian Dim sum carrot white tofu, white tofu bamboo sprout and white tofu mushroom tested for inventiveness. The data collection approach is organoleptic test evaluation and the method used is descriptive quantitative. Questionnaires were distributed in the Lebdosari III RT 02 Rw 05 region. The 81 respondents who participated in the quantitative data analysis evaluated the vegetarian Dim sum made of white tofu, carrots, bamboo shoots, and ear mushrooms. According to the results of the organoleptic test, 54.3% of the respondents liked the taste of the vegetarian Dim sum with bamboo sprouts, while 44.4% liked the smell. The carrot and white tofu vegetarian Dim sum was favored by 25.9% for its appearance and 70.4% for its texture

Empowerment of women households group of poor families to increase income through training to make dimsum in Padang Bulan Village, Medan

Community service activities are carried out through training on how to make dim sum which is carried out for mothers from poor family groups located in Padang Bulan Village, Medan City. Based on data and observations that mothers from poor groups who do not have a job other than taking care of their family, the purpose of this service is to provide training to mothers from poor family groups to make decent dim sum for sale so that they can increase family income. The method in this activity is carried out by socializing and giving lectures to training participants as well as doing hands-on practice on how to make dough for dim sum ingredients and form dim sum properly to sell to consumers. Through the dim sum-making training activities, mothers from poor family groups will become skilled and have the expertise to make and sell dim sum to the community which in turn will increase family income

Symplectic circle actions with isolated fixed points

Consider a symplectic circle action on a closed symplectic manifold with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called weights. We prove that the action is Hamiltonian if the sum of an odd number of weights is never equal to zero (the weights may be taken at different fixed points). Moreover, we show that if $\dim M=6$, or if $\dim M=2n \leq 10$ and each fixed point has weights $\{\pm a_1, \cdots, \pm a_n\}$ for some positive integers $a_i$, it is enough to consider the sum of three weights. As applications, we recover the results for semi-free actions, and for certain circle actions on six-dimensional manifolds

The Pion-Nucleon Coupling Constant in QCD Sum Rules

The pion-nucleon coupling constant $g_{\pi N}$ is studied on the basis of the QCD sum rules. Both the Borel sum rules and the finite energy sum rules for $g_{\pi N}$ are used to examine the effects of higher dimensional operators (up to dim. 7) and $\alpha_s$ corrections in the operator product expansion. Agreement with the experimental number is reached only when $S_{\pi}/S_N$ is greater than one, where $S_{\pi}$ ($S_N$) is the continuum threshold for the $g_{\pi N}$ (nucleon) sum rule.Comment: 15 pages, latex, 9 figures appended as uu-encoded fil

Characteristic Of Hacau Dim Sum Fell Quality Which Was Fortified With Different Seaweed (Eucheuma SP) Flour

The research was intended to evaluate the characteristic of hakau dim sum fell quality witch was fortified with seaweed flour. 10 kg of seaweed was obtained from one of market in pekanbaru was processed to seaweed flour. Hacau dim sum fell was made from tang mine flour, wheat flour, egg, cooking oil, hot water and it was fortified with 0g, 30g, 50g, and 70g of seaweed. Then, for making the contain of dim sum; shrimp, pepper, sugar and salt were prepared. Parameter of this research was observed to folding test, organoleptic, and proximat analysis. The result showed that the fell of hacau dim sum which was fortified with 70g of seaweed flour (R3) was the best treatment with folding test AA, organoleptic value in appearance 8.33, odor 8.33, flavor 3.00, texture 8.33, for moisture content 56.29%, protein content 24.71%, lipid content 9.24%, ash content 2.04% and crude fiber 1.82%