Abstract In this paper, we define the space Sα θ (∆m v, f) of all (∆m v, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ m v and real number α ∈ (0, 1]. We also introduce the space ωα θ (∆m v, f) of all strong (∆m v, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sα θ (∆m v, f) and ωα θ (∆m v, f) are established under certain conditions.

Resumo Objetivo Analisar os resultados clínicos, radiológicos e funcionais da fratura do planalto tibial (Schatzker Tipo V, VI) tratada com fixador externo do anel Illizarov com ou sem abertura mínima. Métodos Um total de 52 fraturas do planalto tibial dos tipos V e VI foram tratadas com fixador externo do anel Ilizarov com ou sem fixação interna mínima. A avaliação do desfecho funcional foi feita utilizando-se o escore da American Knee Society (AKS, na sigla em inglês) com consolidação clínica, radiológica e complicações encontradas. Resultados Foram 37 (71,15%) pacientes do sexo masculino e 15 (28,84%) do sexo feminino, com idade média de 39,07 ± 12,58 anos. Acidentes de trânsito (ATs) foram a principal causa das fraturas, contabilizando 32 casos (61,53%), seguidos por lesão por queda, com 16 casos (30,76%), e impacto direto, com 4 casos (7,69%). Foram 21 (40,38%) casos de fraturas tipo V, 31 (59,61%) casos do tipo VI e 24 (46,15%) casos de fratura exposta. Os escores médios da AKS para as fraturas tipo V e VI foram de 82,8 e 80,70, respectivamente, mas não foi estatisticamente significativo em p <0,05. O escore médio da AKS para fraturas fechadas e abertas também não foi estatisticamente significativo em p <0,05. Conclusões Para a fratura do planalto tibial complexa dos tipos V e VI de Schatzker, a fixação externa de Ilizarov é um método de tratamento seguro, econômico e eficiente que resulta em resultados satisfatórios.

Abstract Objective To analyze the results of clinical, radiological, and functional outcomes of tibial plateau fracture (Schatzker Type V, VI) treated with Illizarov ring external fixator with or without minimum opening. Methods A total of 52 tibial plateau fractures of type V, VI were treated with Ilizarov ring external fixator with or without mininum internal fixation were studied. Functional outcome assessment was done using the American Knee Society (AKS) score with clinical, radiological union, and complications were analyzed. Results There were 37 (71.15%) male and 15 (28.84%) female patients, with a mean age of 39.07 ± 12.58 years old. Road traffic accidents (RTAs) were the major cause of fracture, accounting for 32 cases (61.53%) followed by fall injury, with 16 cases (30.76%), and direct impact, with 4 cases (7.69%). Twenty-one (40.38%) cases were type V and 31 (59.61%) cases were type VI fractures, and there were 24 (46.15%) cases of open fracture. The mean AKS score of Type V and Type VI fractures were 82.8 and 80.70, respectively, but this was statistically not significant at p<0.05. The mean AKS score of closed and open fractures were also statistically not significant at p<0.05. Conclusions For Schatzker Types V and VI complex tibial plateau fractures, Ilizarov external fixation is a safe, cost-effective and efficient treatment method that presents a satisfactory outcome.

Abstract The aqueous solubility of cefixime trihydrate (a water insoluble drug) using different hydrotropic agents was determined and solid dispersions of cefixime trihydrate were prepared by hydrotropic solubilization technique. The drugs content were determined. The aqueous solubility of v was increased many fold in presence of sodium acetate trihydrate as hydrotropic agent. This hydrotropic agent was used to prepare solid dispersion of cefixime trihydrate. Cefixime trihydrate and sodium acetate trihydrate were accurately weighed and taken in a 200 mL beaker. Distilled water 10-15 mL was taken to dissolve hydrotropic agent using heat (48-50 °C). The drug was then added to it and magnetically stirred till whole mass get viscous. The solid dispersions of cefixime trihydrate were characterized by XRD, DSC and IR studies. DSC thermogram, XRD and Infra-Red spectra were studied. Solid dispersions, thus prepared, showed faster release of the drug as compared to pure drug and physical mixture.

Abstract Radioactive trivalent chromium (51Cr3+) is a known radiopharmaceutical used to tag plasma proteins, platelets and also for estimation of blood volume. Nevertheless, there exist insufficient reports with limited sample sizes concerning its clearance from blood and its biodistribution after intravenous administration. This study focused to understand clearance rate of 51Cr3+ from blood and analyze its biodistribution. For biodistribution, six adult New Zealand white albino rabbits were injected with 51Cr3+ through their marginal vein. Percentage clearance of 51Cr3+ from blood was calculated by recording radioactive counts obtained at 1, 58, 61, 120, 180 and 240 minutes post-administration in thirty-three adult New Zealand white albino rabbits. For evaluating 51Cr3+ biodistribution, organs were surgically removed from the rabbits and weighed. Radioactivity of the organs and urine were counted in a nucleonix gamma-ray spectrometer with a NaI scintillation detector. Data were expressed as cps/g. Average clearance of 51Cr3+ was 34% from the first to the 58 minute. Subsequent measurements for hourly clearance at 120, 180 and 240 minutes showed percentage reduction of radioactivity of 33, 14 and 8, respectively. Minimal specific activities were found in the muscle and brain. Spleen, lungs, liver and kidneys exhibited moderate radioactivity. Urine tracer-concentrations were found to be ten times more than that of plasma. From this study, it has been observed that clearance of 51Cr3+ from blood was faster initially which slowed down progressively and there displayed moderate uptake of 51Cr3+ by certain organs. Understanding pharmacokinetics of 51Cr3+ is relevant for its potential use as a diagnostic tool.

A tractor-operated automatic gun sprayer was developed for a cotton crop. The unit consists of frame structure, spray tank, horizontal triplex pump, control valves, spray gun nozzle, pressure gauge, strainer, hydraulic agitator and actuating mechanism. The power to drive the HTP pump was taken from the tractor power take off (PTO) through a belt and pulley. The actuating mechanism consists of motor and worm gear reduction. Two motors with 0.5 kW each (12 V dc) were used to provide oscillation motion to spray guns and motors get power from the tractor battery. The rotation angle of the spray gun is 30° horizontally. Provision was also made to fold the spray boom while in transport. The spray pattern could be adjusted based on the application of chemicals. This study was conducted to determine the suitable nozzle orientation (0°, 15° and 30° downwards) to field crops. The orientation of the spray nozzle was maintained by using the metal protractor. The laboratory experiments were carried out by using the actual cotton plant. The best nozzle orientation for maximum droplet density and droplet size as 15° downward. Leaf hopper [Amrasca biguttula (Ishida)] and aphids [Aphis gossypii (Glover)] control in the cotton crop after 7th day of spraying dinotefuran insecticide from the automatic gun sprayer and conventional tractor-operated gun sprayer was 87, 86 and 58 %, and 50 %, respectively. The total cost required to fabricate the sprayer was US$ 1008. The cost of operation of the tractor operated automatic gun sprayer was found to be US$ 4.7/ ha.

Abstract Objectives To evaluate different types of perianal fistulas and their complications on magnetic resonance imaging (MRI) and to compare plain, contrast, and jelly magnetic resonance fistulography findings. Materials and Methods This prospective study was performed in 30 patients who presented with perianal pus discharge or external fistulous opening. Magnetic resonance imaging of the perianal region before and after giving intravenous contrast and after injecting jelly through a percutaneous opening was performed on a 3T scanner and the results were correlated. Results The mean age of the patients was 40.13±13.88 years (range 19-75 years). The male to female ratio was 14:1. The most common type of fistula was St. James classification type I, which was seen in 13 patients (43%), followed by type IV in 30%, type III in 16%, type II in 6.66%, and type V in 3.33% of the patients. Using agreement analysis, we compared the number of primary and secondary tracts, internal openings, and horseshoe tracts and found a significant agreement between plain and post Jelly MRI fistulography (kappa statistic close to 1).When comparing plain and contrast MRI, there was significant agreement in the primary and secondary tracts, while statistically insignificant results were obtained (p>0.05) for the horseshoe tract and internal openings. Contrast injection was helpful in 7 subjects (23.3%) as peripheral enhancement of abscesses were better delineated. Conclusion Magnetic resonance imaging is the one stop diagnostic modality for perianal fistulas. Acquisition of axial (Ax) T2, axial T2 FS, coronal T2 and coronal T2 FS sequences without administering intravenous contrast or jelly is usually sufficient for the diagnosis of fistulas and their complications.

Abstract For a given graph G, its line graph denoted by L(G) is a graph whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 and e2 are incident to a common vertex in G. Let R be a finite commutative ring with nonzero identity and G(R) denotes the unit graph associated with R. In this manuscript, we have studied the line graph L(G(R)) of unit graph G(R) associated with R. In the course of the investigation, several basic properties, viz., diameter, girth, clique, and chromatic number of L(G(R)) have been determined. Further, we have derived sufficient conditions for L(G(R)) to be Planar and Hamiltonian.

Abstract Let G = (V,E) be a simple graph. An edge e ∈ E(G) edge-vertex dominates a vertex v ∈ V (G) if e is incident with v or e is incident with a vertex adjacent to v. A subset D ⊆ E(G) is an edge-vertex dominating set of a graph G if every vertex of G is edge-vertex dominated by an edge of D. A vertex cover of G is a set C ⊆ V such that for each edge uv ∈ E at least one of u and v is in C. We characterize trees with edge-vertex domination number equals vertex covering number.

Abstract A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices. The vertex-edge Roman domination number of a graph G, denoted by γ veR (G), is the minimum weight of a ve-RDF G. We characterize trees with vertexedge roman domination number equal to twice domination number minus one.

Abstract. The electrochemical studies of picric acid were carried out in acidic, neutral and basic buffer media at bare glassy carbon (GC) and polypyrrole modified GC electrode. Cyclic Voltammogram (CV) of picric acid exhibited three reduction peaks at -0.4, -0.8 and -1.5V (vs. Ag/AgCl) and two oxidation peaks at 0.8 and 1.4V (vs. Ag/AgCl). Among the various pH studied, highly sensitive response was observed at pH 1.0. The effect of scan rate was studied between 25 and 500 mVs-1 at the optimal pH.CV results revealed the adsorption-controlled reaction at the electrode surface. The GC electrode was modified with polypyrrole conducting polymer film to enhance the electrocatalytic activity of the reductive species. Atomic force microscopy (AFM) images showed the nanosphere morphology of the polypyrrole film, which was coated uniformly on the electrode surface. Under optimum experimental conditions, the influence of concentration on the stripping signal was studied. The linear range of detection was found between 50 ppb and 250 ppb with the lower limit of detection of 10±3 ppb.

Resumen. Los estudios electroquímicos del ácido pícrico se realizaron en medios amortiguados ácidos, neutros y alcalinos con un electrodo de carbono vítreo (GC) y de GC modificado con polipirrol (PP). El voltamperograma cíclico (CV) del ácido pícrico mostró tres picos de reducción a -0.4, -0.8 y -1.5 V (frente a Ag/AgCl) y dos picos de oxidación a 0.8 y 1.4 V (frente a Ag/AgCl). Entre los diversos valores de pH estudiados, se observó una respuesta altamente sensible a pH de 1.0. El efecto de la velocidad de barrido se estudió entre 25 y 500 mVs-1 en el pH óptimo. Los resultados de CV revelaron que la reacción está controlada por adsorción en la superficie del electrodo. El electrodo de GC fue modificado con una película polimérica conductora de PP para mejorar la actividad electrocatalítica de las especies. Las imágenes de la microscopía de fuerza atómica (AFM) mostraron la morfología de la nanoesfera de la película de PP, que recubre uniformemente la superficie del electrodo. Bajo condiciones experimentales óptimas, se estudió la influencia de la concentración en la señal de stripping. El rango lineal de detección se encontró entre 50 ppb y 250 ppb con el límite inferior de detección de 10±3 ppb.

Abstract: A vertex v of a graph G = (V,E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set if every edge of E is ve-dominated by at least one vertex of S. The minimum cardinality of a vertex-edge dominating set of G is the vertex-edge domination number γve(G) . In this paper we prove (γt(T)−ℓ+1)/2 ≤ γve(T) ≤(γt(T)+ℓ−1)/2 and characterize trees attaining each of these bounds.

RESUMO Introdução: O objetivo deste estudo foi analisar a apresentação e tratamento de grande trauma renal em crianças. Método: Foi realizado um estudo retrospectivo incluindo dados coletados dos pacientes que foram internados na cirurgia pediátrica com lesão renal de grau importante (grau 3 ou mais) de janeiro de 2015 a agosto de 2018. Coletamos dados a respeito de demografia, parâmetros clínicos, manejo, tempo de internação e resultado final. Resultados: Das 13 crianças (9 homens e 4 mulheres) com faixa etária de 2-12 anos (média de 8 anos), a queda auto-relatada foi o modo de lesão mais comum seguido de acidente de trânsito. A maioria (10/13, 75%) apresentou lesão renal direita. Oito crianças tiveram uma lesão grau IV, uma apresentou uma lesão grau V e quatro crianças apresentaram lesão grau III. A duração da internação hospitalar variou de 3 a 28 (média de 11,7) dias. Três crianças necessitaram de transfusão de sangue. Uma criança necessitou de aspiração guiada por imagem duas vezes e duas inserções de dreno pigtail exigidas para coleções perinefréticas. Todas as 13 crianças melhoraram sem re-internação ou necessidade de qualquer outra intervenção cirúrgica. Conclusão: Crianças com trauma renal de alto grau devido a lesão contusa podem ser manejadas com sucesso sem intervenção cirúrgica, e intervenção mínima pode ser necessária apenas em situações selecionadas.

ABSTRACT Introduction: The aim of this study was to analyze the presentation and management of major grade renal trauma in children. Method: A retrospective study was performed including data collected from the patients who were admitted in Pediatric surgery with major grade renal injury (grade 3 and more) from January 2015 to August 2018. Demography, clinical parameters, management, duration of hospital stay and final outcome were noted. Results: Out of 13 children (9 males and 4 females), with age range 2-12 years (mean of 8 years), reported self-fall was the commonest mode of injury followed by road traffic accident. The majority (10/13, 75%) had a right renal injury. Eight children had a grade IV injury, one had a grade V injury, and four children had grade III injury. Duration of hospital stay varied from 3 to 28 (mean of 11.7) days. Three children required blood transfusion. One child required image guided aspiration twice and two required pigtail insertion for perinephric collection. All the 13 children improved without readmission or need for any other surgical intervention. Conclusion: Children with major grade renal trauma due to blunt injury can be successfully managed without surgical intervention and minimal intervention may only be needed in select situations.

ABSTRACT Purpose To study the intraoperative findings in case of early and delayed decompression of facial nerve paralysis and compare their results. Methods Retrospective data analysis of 23 cases of longitudinal temporal bone fracture with House-Brackmann grade V and VI facial nerve paralysis. All cases were thoroughly evaluated and underwent facial nerve decompression through the transmastoid approach. All cases were under regular follow-up till the date of manuscript submission. Results Clinical improvement of the facial nerve function was observed for early vs. delayed facial nerve decompression. In the early decompression group, facial nerve function improved to grade II in eight cases (80%) and grade III in two cases (20%), whereas in the delayed decompression group it improved to grade II in one case (7.70%), grade III in four cases (30.76%), grade IV in seven cases (53.84%), and grade V in one case (7.70%). Conclusions Early decompression of facial nerve provides better results than delayed decompression because it enables early expansion of the nerve.

Abstract A three-dimensional elastic-plastic finite element analysis (FEA) is carried out to estimate the rolling contact fatigue (RCF) crack initiation life for varied slip range on the rail arising from operational variations. The wheel load produces Hertzian contact pressure. Variation in engine traction induces slip variations that evolves thermal load in terms of heat flux. The aperiodic rolling of wheel on rail develops non-proportional multiaxial fatigue loading. Present study combines these effects by translating the wheel load on rail for multiple (twelve) pass in presence of thermal load, contact pressure and traction through a proposed simulation. The temperature dependent Chaboche material model with nonlinear kinematic hardening law is implemented to estimate the stresses and plastic strains governing the multiaxial fatigue condition at the interface. The location of maximum von Mises stress, found at a material point on or a layer below the rail-head, contemplates the fatigue crack initiation site. A coded search algorithm helps to identify the critical plane of crack initiation corresponding to the maximum fatigue parameter (FP). In contrast to available predictions of RCF life considering contact pressure and/or traction or frictional heat in isolation, present study combines all these loads together and provides a more realistic result by numerical simulation.

The gingiva is often the site of localized growths that are considered to be reactive rather than neoplastic in nature. One of these gingival lesions, seen rather infrequently, is peripheral ossifying fibroma (POF) a condition that predominantly affects women and is usually located in the anterior maxilla. The lesions are pink to red in colour, and firm to hard in consistency depending on their bone content. As enlargement occurs, they may become ulcerated. Concurrent poor oral hygiene and early periodontal disease are commonly seen. In most cases there is no underlying bone involvement evident on the radiograph. The definitive diagnosis is established by histological examination, which reveals the presence of cellular connective tissue with focal calcifications. Surgical excision is the treatment of choice, though the recurrence rate can reach 20%. This article presents a case of POF in a 14yearold female, from whom the tumour was excised using electrosurgery.