INTRODUCTIONMalaria remains a serious health problem in many parts of the world. It causes high morbidity and claims many lives in developing countries each year. Humans are generally infected by four species of malaria parasites. 1Malarial acute kidney injury is commonly found in nonimmune adults and older children with falciparum malaria and occasionally with Plasmodium vivax. Occurrence of malaria induced acute kidney injury in severe falciparum malaria is quite common in Southeast Asia and Indian subcontinent where intensity of malaria transmission is usually low.2 Major manifestations of severe malaria in children are cerebral malaria, severe ABSTRACTBackground: Aim of current study was to assess the epidemiology, clinico-biochemical spectrum and prognosis of acute malaria induced nephropathy in children. Methods: This was a prospective study conducted in the period from November 2013 to November 2014 in children suffering from acute malaria induced acute kidney injury. Malaria was confirmed by peripheral blood film or Rapid malaria test and detailed clinical evaluation and investigations were carried out to find multi-organ afflictions with special emphasis on renal involvement. Results: Out of total 200 cases with malaria recorded in our hospital 60 (30%) cases had acute malaria induced acute kidney injury caused by Plasmodium vivax in 45 (75%), Plasmodium falciparum in 3 (5%) and mixed infection in 12 (20%) cases. Thirty percentage of cases had come from Sri Ganganagar district making it the most common geographical region in our study. The sex ratio was 3.6:1. Most common age group was 5-10 year age group contributing to 45% of the cases. Fever and oliguria being the most common presentation and was observed in all the cases followed by vomiting, pain abdomen and hypotension which was present in 33%, 32% and 20% of the cases respectively. Oliguria was present in all the cases in which 24 (40%) cases had urine output <1 ml/kg/hour, 36 (60%) patient had urine output <0.5 ml/kg/hour with G.F.R >25 ml/min/1.73m 2 and <25 ml/min/1.73m 2 seen in 40 (66%) and 3 (5%) cases respectively. Fifty five patients (91.66%) had S. creatinine between 1.5-3 mg/dl and only 5 patients (8.33%) had serum creatinine >3 mg/dl. 75% cases recovered in <5 days and 4 patients expired, 2 due to respiratory failure and 2 due to MODS and cerebral malaria. expired cases two were died due to respiratory failure, other two were died due to multiorgan failure and cerebral malaria. Conclusions: The spectrum of renal involvement due to malaria is variable ranging from mild derangement of renal functions to advanced stage of renal dysfunction which needs immediate dialysis. Severe renal involvement was mainly seen with P. falciparum but in our study it is mainly seen with P. vivax infection.

Wilson frames{ψjk:w0,w-1∈L2(ℝ)}j∈ℤ,k∈ℕ0as a generalization of Wilson bases have been defined and studied. We give necessary condition for a Wilson system to be a Wilson frame. Also, sufficient conditions for a Wilson system to be a Wilson Bessel sequence are obtained. Under the assumption that the window functionsw0andw-1for odd and even indices ofjare the same, we obtain sufficient conditions for a Wilson system to be a Wilson frame (Wilson Bessel sequence). Finally, under the same conditions, a characterization of Wilson frame in terms of Zak transform is given.

Given that the Gabor system {E mb Tnag} m,n∈Z is a Gabor frame for L 2 (R), a sufficient condition is obtained for the Gabor system {E mb TnaHg} m,n∈Z to be a Gabor frame, where Hg denotes the Hilbert transform of g ∈ L 2 (R). It is proved that the Hilbert transform operator and the frame operator for the Gabor Bessel sequence {E mb Tnag} m,n∈Z commute with each other under certain conditions. Also, a sufficient condition is obtained for the Wilson system {ψ k,n Hg} k∈Z n∈N 0 to be a Wilson frame given that {ψ k,n g} k∈Z n∈N 0 is a Wilson frame. Finally, we obtain conditions under which the Hilbert transform operator and the frame operator for the Wilson Bessel sequence {ψ k,n g} k∈Z n∈N 0 commute with each other.Example 3.1. Consider the function g = cos( 2πx 3 )χ [0, 3 4 ] ∈ L 2 (R), then it is easy to observe that {E mb T na g} m,n∈Z and {E mb T na Hg} m,n∈Z are both Gabor frames for 0 < a < 3 4 and 0 < b ≤ 4 3 . It is natural to raise the following general question.Problem: Let g ∈ L 2 (R) be such that {E mb T na g} m,n∈Z is a Gabor frame. Is {E mb T na Hg} m,n∈Z a Gabor frame?The answer to this problem is negative.Example 3.2. If g = χ [0,1] , then {E m T n g} m,n∈Z is a Gabor frame but {E m T n Hg} m,n∈Z is not a Gabor frame.

In this paper, we define the discrete time Wilson frame (DTW frame) for l 2 ℤ and discuss some properties of discrete time Wilson frames. Also, we give an interplay between DTW frames and discrete time Gabor frames. Furthermore, a necessary and a sufficient condition for the DTW frame in terms of Zak transform are given. Moreover, the frame operator for the DTW frame is obtained. Finally, we discuss dual pair of frames for discrete time Wilson systems and give a sufficient condition for their existence.

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