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Search Results: 1 - 10 of 2223 matches for " Deepak Bansal "
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Fekete-Szeg? Problem for a New Class of Analytic Functions
Deepak Bansal
International Journal of Mathematics and Mathematical Sciences , 2011, DOI: 10.1155/2011/143096
Abstract: We consider the Fekete-Szeg? problem with complex parameter for the class ( ) of analytic functions. 1. Introduction and Preliminaries Let denote the class of functions of the form which are analytic in the open unit disk and denote the subclass of that are univalent in . A function in is said to be in class of starlike functions of order zero in , if for . Let denote the class of all functions that are convex. Further, is convex if and only if is star-like. A function is said to be close-to-convex with respect to a fixed star-like function if and only if for . Let denote of all such close-to-convex functions [1]. Fekete and Szeg? proved a noticeable result that the estimate holds for any normalized univalent function of the form (1.1) in the open unit disk and for . This inequality is sharp for each (see [2]). The coefficient functional on normalized analytic functions in the unit disk represents various geometric quantities, for example, when , , becomes , where denote the Schwarzian derivative of locally univalent functions in . In literature, there exists a large number of results about inequalities for corresponding to various subclasses of . The problem of maximising the absolute value of the functional is called the Fekete-Szeg? problem; see [2]. In [3], Koepf solved the Fekete-Szeg? problem for close-to-convex functions and the largest real number for which is maximised by the Koebe function is , and later in [4] (see also [5]), this result was generalized for functions that are close-to-convex of order . Let be an analytic function with positive real part on with , which maps the unit disk onto a star-like region with respect to 1 which is symmetric with respect to the real axis. Let be the class of functions in for which and be the class of functions in for which where denotes the subordination between analytic functions. These classes were introduced and studied by Ma and Minda [6]. They have obtained the Fekete-Szeg? inequality for the functions in the class . Motivated by the class in paper [7], we introduce the following class. Definition 1.1. Let , . A function is in th class , if where is defined the same as above. If we set in (1.6), we get which is again a new class. We list few particular cases of this class discussed in the literature for was discussed recently by Swaminathan [7]. The class for , where is considered in [8] (see also [9]). The class with was considered in [10] with reference to the univalencey of partial sums. whenever , the class considered in [11]. For geometric aspects of these classes, see the corresponding
Coefficients bounds in some subclass of analytic functions
Janusz Sokol,Deepak Bansal
Tamkang Journal of Mathematics , 2012, DOI: 10.5556/j.tkjm.43.2012.621-630
Abstract: In this paper we consider a class of analytic functions introduced by Mishra and Gochhayat, {it Fekete-Szeg"o problem for a class defined by an integral operator}, Kodai Math. J., 33(2010) 310--328, which is connected with $k$-starlike functions through Noor operator. We find inclusion relations and coefficients bounds in this class.
Atypical teratoid/rhabdoid tumors of central nervous system
Bansal K,Goel Deepak
Journal of Pediatric Neurosciences , 2007,
Abstract: Aims and Objectives: To review the clinical features and current understanding of the epidemiology, biology and management of pediatric atypical teratoid/rhabdoid tumors and analyzing the different treatment modalities. Materials and Methods: The MEDLINE database, bibliographies of selected articles and current English-language texts on the subject were reviewed. A Pubmed search was made with keywords pediatric atypical teratoid/rhabdoid tumors, intracranial, surgery, chemotherapy and radiotherapy. Most recent articles and also significant older articles having all above said words were selected and their results were reviewed in detail. Results: Atypical teratoid/rhabdoid tumors (AT/RT) of the central nervous system (CNS) most frequently diagnosed in smaller than 3 years of age and incidence is 1-2% of all brain tumors in children. 63% of the AT/RT of the CNS is seen in infra-tentorial compartment, there are no precise imaging features that differentiate AT/RT from the other posterior fossa tumor. The "rhabdoid" cells are characteristic on cytopathology. It has been established now that CNS, AT/RT often show deletion of the long arm of chromosome 22q11.2. The initial treatment for most children with AT/RT is surgical with and without cerebrospinal fluid diversionary procedure. Children with less than 3 years of age offered chemotherapy but in older children radiotherapy is given in addition.
Coefficient estimates and subordination properties associated with certain classes of functions
R. K. Raina,Deepak Bansal
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.3685
Abstract: This note investigates coefficient estimates and subordination properties for certain classes of normalized functions (which are essentially defined by means of a Hadamard product of two analytic functions). We exhibit several interesting consequences of our main results, and in the process, we are also led to the corrected forms of the results given by Owa and Nishiwaki (2002).
Some subordination theorems associated with a new operator
Deepak Bansal,Ravindar K. Raina
Le Matematiche , 2010,
Abstract: In this paper we introduce a linear operator and obtain certain differential subordination properties associated with this linear operator. Some relevant consequences of the main results including new variations of earlier known results are also pointed out.
Every non-obstructive hydrocephalus is not due to tuberculous basal meningitis
Goel Deepak,Bansal K,Mittal Manish,Ranjeet
Annals of Indian Academy of Neurology , 2010,
Unresectable gastrointestinal stromal tumors
Menon Prema,Bansal Deepak,Rao KLN
Journal of Indian Association of Pediatric Surgeons , 2011,
Conjoint bicondylar Hoffa fracture in a child: a rare variant treated by minimally invasive approach
Hitesh Lal,Pankaj Bansal,Rahul Khare,Deepak Mittal
Journal of Orthopaedics and Traumatology , 2011, DOI: 10.1007/s10195-011-0133-3
Abstract: A case of conjoint Hoffa-type fracture in a child is presented. Hoffa fracture, i.e., coronal slice fracture of the condyles of the femur, is rare in adults and even rarer in the pediatric population. To date, no case of conjoint bicondylar Hoffa fracture has been reported in the literature. The presented case was successfully treated by arthroscopically assisted internal fixation.
Statistical Analysis of Human Physiological Parameter using Six Sigma Techniques
Dipali Bansal,Munna Khan,Deepak Goel,A. K. Salhan
Lecture Notes in Engineering and Computer Science , 2008,
Mediterranean Journal of Hematology and Infectious Diseases , 2012, DOI: 10.4084/mjhid.2012.
Abstract: Introduction: The MPAL comprise 2-5% of all acute leukemia. The present WHO 2008 classification has separated two groups in MPAL based on t(9;22) positivity and MLL rearrangement. Aims & Objectives: The aim of the present pilot study is to note the incidence of BCR-ABL transcript in MPAL cases using the RT-PCR assay and to correlate the status with hematological remission post induction. Materials & Methods: A total of 10 MPAL cases classified on Flow-cytometry based on the current WHO 2008 criteria were enrolled. In all the cases Bone marrow or peripheral blood sample in EDTA was processed for molecular studies and the RT-PCR reaction carried out using primers specific to the t (9;22) and t(4;11) translocation. The post induction check marrow slides were also reviewed. Results: Out of the total 10 MPAL cases, 7/10 (70%) were adult and 3/10 (30%) pediatric cases. A total of 4/10 (40%) cases showed positivity for the t(9;22) transcript and none for t (4;11). Of the 4 positive cases, 3/10(30%) were adult cases and 1/10(10%) pediatric case. The BCR-ABL transcript type in adult cases was b3a2 (p210) in 2/3 (66%) and e1a2 (p190) in 1/3 (33.3%) case. The single pediatric case was positive for b3a2 transcript. Discussion & Conclusion: All the 4 positive MPAL cases presented with high TLC and low platelet count (p<0.05). The positive cases also showed hematological remission at post induction check marrow (blasts<5%). This could partly be explained due to good response to the imatinib added to the treatment protocol.
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