Some vanishing sums involving binomial coefficients in the denominator

Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by William Horrace [1] using probability theory turn out to be special cases of the Chu-Vandermonde identities. Here, we obtain some generalizations of the identities observed by Horrace and give different types of proofs; these, in turn, give rise to some other new identities. In particular, we evaluate sums of the form Pm j=0 (1) j j d (mj) (n+jj ) and deduce that they vanish when d is even and m = n > d=2. It is well-known [2] that sums involving binomial coeffcients can usually be expressed in terms of the hypergeometric functions but it is more interesting if such a function can be evaluated explicitly at a given argument. Identities such as the ones we prove could perhaps be of some interest due to the explicit evaluation possible. The papers [3], [4] are among many which deal with identities for sums where the binomial coeffcients occur in the denominator and we use similar methods here

Spatial Modeling of Cold Lava Flood Evacuation in Kali Putih, Magelang Regency, Using Network Analyst

The event of Mount Merapi\u27s phreatic eruption, at least reminds us that the riverbank of Kali Putih which is located in Magelang Regency, Central Java Province has not been completely free from the threat of cold lava flood, especially during the rainy season. Therefore, a preventive action in relation to cold lava flood mitigation matters needs to be done. As part of the preventive action, a spatial modeling was carried out in Kali Putih to get an overview of the number and distribution of affected residential areas, the location and distribution of temporary evacuation sites (TES), the most effective number of final evacuation sites (FES), and various evacuation routes formed. Modeling began by calculating the level of vulnerability of cold lava in Sub Watershed of Kali Putih to get the most vulnerable areas for cold lava flood. 3D analyst and spatial analyst were used at this stage. The analysis was continued to calculate the number of affected settlements, using vector-based analysis. Furthermore, the determination of the number and distribution of TES, the number and distribution of FES, and determination of evacuation routes were carried out using Network Analyst. From this spatial modeling, the following results were obtained: 66 out of 179 residential areas were most likely affected by cold lava flood, 23 temporary evacuation sites (TES), and 7 final evacuation sites (FES), 57 evacuation routes from affected settlements to TES, and 22 evacuation routes from TES to FE

The diagnostic value of lymph node biopsy to detect Castleman’s disease

HIV is not indicated in the aetiology of Castleman’s disease. However, it impacts on the prevalence and natural history of this disease and significantly on the disease progression. Castleman’s disease is a uni- or multicentric disease of the lymph node with or without polyclonal proliferation of B-cells. It is a morphologically distinct form of lymph node hyperplasia and is characterised by significant architectural changes in all lymphatic compartments. Histopathologically, the disease is classified into two major subtypes: the hyaline-vascular type and the plasma-cell type. A mixed type is also identified, as there are frequent transitions between the types. The diagnosis of Castleman’s disease needs to be made histologically. Treatment modalities include surgery, which is curative for unicentric disease, and systemic therapy, which is needed for multicentric disease. This case highlights the diagnostic value of lymph node excision biopsy in HIV-infected patients

Eigenforms of half-integral weight

Let k be an odd integer and N a positive integer such that 4 | N. Let X be a Dirichlet character modulo N. Shimura decomposes the space of half-integral weight forms Sk/2(N,X) as Sk/2(N,X) = S0(N,X)oOΦSk/2(N,X,Φ) where Φ runs through the newforms of weight k-1 and level dividing N/2 and character X2; Sk/2(N,X,Φ) is the subspace of forms that are Shimura-equivalent to Φ; and S0(N,X) is the subspace generated by single-variable theta-series. We give an explicit algorithm for computing this decomposition. Once we have the decomposition, we can exploreWaldspurger's theorem expressing the critical values of the L-functions of twists of an elliptic curve in terms of the coefficients of modular forms of half-integral weight. Following Tunnell, this often allows us to give a criterion for the n-th twist of an elliptic curve to have positive rank in terms of the number of representations of certain integers by certain ternary quadratic forms

The Growth Mindset of Undergraduate Students Studying Education Programs

Abstract. Growth Mindset is one of the determinants of a person's success in study and career. This is because people who have a growth mindset have perseverance, like challenges, and believe that their abilities will improve if they practice persistently. This quantitative study explores the growth mindset of undergraduate students studying education programs with a descriptive analysis and compares the growth mindset of students from private and public universities with independent sample t-test analysis. There were 452 undergraduate students from various universities in South Sulawesi participating: 215 students from private universities and 237 students from public universities. The results showed that the growth mindset of undergraduate students in education programs was high, both in private and public universities. However, there is a difference between the two, where the growth mindset of undergraduate students in public universirties is higher than that in private universities

Collapse/Flattening of Nucleonic Bags in Ultra-Strong Magnetic Field

It is shown explicitly using MIT bag model that in presence of ultra-strong magnetic fields, a nucleon either flattens or collapses in the direction transverse to the external magnetic field in the classical or quantum mechanical picture respectively. Which gives rise to some kind of mechanical instability. Alternatively, it is argued that the bag model of confinement may not be applicable in this strange situation.Comment: 8 pages, REVTEX, 3 figures .eps files (included

Gravitational collapse due to dark matter and dark energy in the brane world scenario

Gravitational collapse of FRW brane world embedded in a conformaly flat bulk is considered for matter cloud consists of dark matter and dark energy with equation of state $p=\epsilon \rho$ $(\epsilon<-{1/3})$. The effect of dark matter and dark energy is being considered first separately and then a combination of them both with and without interaction. In some cases the collapse leads to black hole in some other cases naked singularity appears.Comment: 10 Latex Pages, RevTex style, 4 figure