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

Assessment Of Temporal And Spatial Alterations In Spinal Glial Reactivityand The Extent Of Cervical Spinal Axonal Injury In The Rat After Blast Overpressure

Blast induced neurotrauma (BINT) is the signature wound of veterans returning from various military operations. A substantial percentage of Operations Enduring Freedom (OEF) and Iraqi Freedom (OIF) veterans have reported to experience ongoing or new pain following their military service. Head (58%) and back (55%) have been the high prevailing locations of pain in these returning OIF and OEF veterans and the underlying pathomechanism of these conditions is yet to be understood. In the context of blast overpressure induced pathological changes, the fundamental question that still needs to be addressed is whether there are any underlying cellular injury changes the spinal cord following blast. If proven, it is postulated that cellular injury changes in the form of glial activation may contribute to neuronal sensitization and altered sensation through the release of various inflammatory mediators. Much of the previous and ongoing research studies have been directed at understanding blast induced changes in the brain alone with changes in the spinal cord still remaining an enigma. Accordingly, as a first step, we attempted to investigate spatial and temporal alterations in glial activation in the spinal cord following blast exposure. In addition, we also attempted to study the presence of axonal injury in the cervical spinal cord following blast overpressure. As part of this investigation, anaesthetized male Sprague Dawley rats were subjected to a single insult of blast overpressure (22psi)using a helium driven shock tube. The rats were divided into two groups; Sham and Blast with acute and sub-acute survival periods; 6hrs, 24hrs, 3days and 7days respectively. Glial activation was assessed by GFAP (Glial Fibrillary Acidic Protein) and IBA1 (Ionized Calcium Binding Molecule 1) immunohistochemistry. GFAP and Iba1 are routinely used to investigate astrocytic and microglial activation in the brain and spinal cord. Axonal injury in the cervical spinal cord was assessed by β-APP (Beta Amyloid Precursor Protein) immunohistochemistry. β-APP is a commonly used marker to detect the presence of diffuse axonal injury in the brain. Behaviorally, blast exposed rats exhibited significantly increased surface righting duration compared to sham rats. Our immunohistochemistry results indicate differential activation of astrocytes and microglia in various spinal cord regions in blast exposed group compared to sham. Rats subjected to blast overpressure showed increased expression of astrocytes and microglia at acute and sub-acute periods. Evidence of diffuse axonal injury also observed in the cervical spinal cord following the blast overpressure. Taken together, our results suggest that blast exposure in a craniocephalic orientation in rats resulted an enhanced spinal glial reactivity as well as cervical spinal axonal injury. We postulate that injury changes in the form of activation of astrocytes and microglia with diffuse axonal injury may contribute to the release of various inflammatory mediators which may in turn be related to the ensuing sensory changes. These results lay foundation to further studies on blast related injury changes in the spinal cord

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

Udarni presjeci dvoelektronskog uhvata iz helijevih atoma u osnovno stanje golih upadnih iona

Double charge-transfer cross-sections from ground state of helium atoms by multiply-charged bare ions have been studied in the energy range 50 - 200 keV/amu to investigate the dependence of cross-sections on the charge state of different ions (He2+, Li3+, Be4+, B5+, C6+, N7+ and O8+). In our calculation, we have employed the four-body boundary-corrected continuum intermediate state (BCCIS-4B) approximation. The variation of double charge transfer cross sections of bare ions into the ground state is displayed versus the incident projectile energy. Due to the non-availability of any theoretical and experimental findings in that energy range for collision systems under study (Be4+, B5+, C6+, N7+ and O8+ + He), we can not compare the present results with other data. We have also analysed differential double-capture cross sections for the collision of a-particle with helium atom at 1500 keV. The obtained results for the differential double-capture cross sections into the ground state are compared with the experimental data and a satisfactory agreement has been obtained.Proučavamo udarne presjeke za prijelaz dvaju elektrona u osnovnom stanju helija u upadne potpuno gole ione energije 50 – 200 keV/amu radi istraživanja ovisnosti udarnih presjeka o višestrukosti ionizacije upadnih iona (He2+, Li3+, Be4+, B5+, C 6+, N7+ i O8+). Primijenili smo približenje međustanja u kontinuumu s graničnom popravkom za četiri tijela (BCCIS-4B). Predstavljamo energijsku ovisnost udarnih presjeka za prijelaz dvaju elektrona u osnovnom stanju helija u upadne potpuno gole ione. Zbog manjka teorijskih i eksperimentalnih podataka o proučavanim sustavima (Be4+, B5+, C6+, N7+ and O8+ + He) u tom području energije nismo u mogućnosti načiniti usporedbe s drugim podacima. Također smo analizirali diferencijalne udarne presjeke za dvostruki uhvat u sudaru α-čestice s helijevim atomom na 1500 keV. Postignuti ishodi za diferencijalne udarne presjeke dvojnog uhvata se uspoređuju s eksperimentalnim podacima i postignuto je dobro slaganje

Udarni presjeci dvoelektronskog uhvata iz helijevih atoma u osnovno stanje golih upadnih iona

Double charge-transfer cross-sections from ground state of helium atoms by multiply-charged bare ions have been studied in the energy range 50 - 200 keV/amu to investigate the dependence of cross-sections on the charge state of different ions (He2+, Li3+, Be4+, B5+, C6+, N7+ and O8+). In our calculation, we have employed the four-body boundary-corrected continuum intermediate state (BCCIS-4B) approximation. The variation of double charge transfer cross sections of bare ions into the ground state is displayed versus the incident projectile energy. Due to the non-availability of any theoretical and experimental findings in that energy range for collision systems under study (Be4+, B5+, C6+, N7+ and O8+ + He), we can not compare the present results with other data. We have also analysed differential double-capture cross sections for the collision of a-particle with helium atom at 1500 keV. The obtained results for the differential double-capture cross sections into the ground state are compared with the experimental data and a satisfactory agreement has been obtained.Proučavamo udarne presjeke za prijelaz dvaju elektrona u osnovnom stanju helija u upadne potpuno gole ione energije 50 – 200 keV/amu radi istraživanja ovisnosti udarnih presjeka o višestrukosti ionizacije upadnih iona (He2+, Li3+, Be4+, B5+, C 6+, N7+ i O8+). Primijenili smo približenje međustanja u kontinuumu s graničnom popravkom za četiri tijela (BCCIS-4B). Predstavljamo energijsku ovisnost udarnih presjeka za prijelaz dvaju elektrona u osnovnom stanju helija u upadne potpuno gole ione. Zbog manjka teorijskih i eksperimentalnih podataka o proučavanim sustavima (Be4+, B5+, C6+, N7+ and O8+ + He) u tom području energije nismo u mogućnosti načiniti usporedbe s drugim podacima. Također smo analizirali diferencijalne udarne presjeke za dvostruki uhvat u sudaru α-čestice s helijevim atomom na 1500 keV. Postignuti ishodi za diferencijalne udarne presjeke dvojnog uhvata se uspoređuju s eksperimentalnim podacima i postignuto je dobro slaganje

Schwannoma in an accessory branch of the posterior cord of the brachial plexus: a rare case report

Background: Variation in the posterior cord of the brachial plexus is complicated and creates a risky relationship with the neighbouring structures. This is of importance to the surgeons, anaesthetists who must deal with the region in surgeries and procedures. Moreover, any benign tumour like Schwannoma is rare in the plexus comprising 5 % of total head and neck schwannomas. Methods: We present a case of Schwannoma of the brachial plexus in a cadaver during routine anatomy dissection for the medical students. The origin and order of branching of the posterior cord were recorded and photographs were taken. The tumour was present in an accessory branch of the posterior cord and removal was made in-toto. An immunohistochemistry study was done for confirmation of diagnosis. Results: The classical branching of the posterior cord was present. Additionally, a branch existed that was supplying the triceps muscle and emerged directly from the posterior cord. Tumour having the dimension of 2 x 1.8x 0.5 cm was present. Conclusions: Schwannomas are indolent but may cause compression of the nerve and resulting neurological symptoms. They might mimic nodules of supraclavicular fossa in breast carcinoma. Variations of the brachial plexus can also make the surgeons confused during surgery due to which anatomical knowledge of the possible variations is important. Pre- and Post-operative complications can be easily predicted from it. Follow-up of the tumour is essential to track its progress and differentiation

Identification of miR-379/miR-656 (C14MC) cluster downregulation and associated epigenetic and transcription regulatory mechanism in oligodendrogliomas

Introduction Although role of individual microRNAs (miRNAs) in the pathogenesis of gliomas has been well studied, their role as a clustered remains unexplored in gliomas. Methods In this study, we performed the expression analysis of miR-379/miR-656 miRNA-cluster (C14MC) in oligodendrogliomas (ODGs) and also investigated the mechanism underlying modulation of this cluster. Results We identified significant downregulation of majority of the miRNAs from this cluster in ODGs. Further data from The Cancer Genome Atlas (TCGA) also confirmed the global downregulation of C14MC. Furthermore, we observed that its regulation is maintained by transcription factor MEF2. In addition, epigenetic machinery involving DNA and histone-methylation are also involved in its regulation, which is acting independently or in synergy. The post- transcriptionally regulatory network of this cluster showed enrichment of key cancer-related biological processes such as cell adhesion and migration. Also, there was enrichment of several cancer related pathways viz PIK3 signaling pathway and glioma pathways. Survival analysis demonstrated association of C14MC (miR-487b and miR-409-3p) with poor progression free survival in ODGs. Conclusion Our work demonstrates tumor-suppressive role of C14MC and its role in pathogenesis of ODGs and therefore could be relevant for the development of new therapeutic strategies

On Online Banking Authentication for All: A Comparison of BankID Login Efficiency Using Smartphones Versus Code Generators

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Vertical migration of some herbicides through undisturbed and homogenized soil columns

A laboratory experiment was conducted by using three herbicides, two from dinitroaniline group and one from thiocarbamate group to know their degree of downward movement (leachability) through soil columns and their contribution in ground water contamination. Soil columns were loaded with Pendimethalin, Benthiocarb and Oryzalin at doses of 10.0, 10.0 and 7.7 kg/ha, respectively. After 30 days soil samples were analyzed from each segments (i.e. 0–6, 6–12, 12–18, 18–24 and 24–30 cm) for Benthiocarb and Pendimethalin by GLC equipped with Ni63 electron capture detector (ECD) and for Oryzalin by HPLC coupled with UV-VIS detector. The results obtained in the present study reveal that the residues of the three herbicides under investigation were predominantly confined to the upper soil layer (0–6 cm). Comparatively, low mobility of these herbicides in soils could be due to strong adsorption of these chemical to soil colloids