On the sum of the <i>k</i> largest eigenvalues of graphs and maximal energy of bipartite graphs

Das, Kinkar Chandra,Mojallal, Seyed Ahmad,Sun, Shaowei Elsevier 2019 Linear algebra and its applications Vol.569 No.-

<P><B>Abstract</B></P> <P>Let <I>G</I> be a graph of order <I>n</I>. Also let <SUB> λ 1 </SUB> ≥ <SUB> λ 2 </SUB> ≥ ⋯ ≥ <SUB> λ n </SUB> be the eigenvalues of graph <I>G</I>. In this paper, we present the following upper bound on the sum of the <I>k</I> ( ≤ n ) largest eigenvalues of <I>G</I> in terms of the order <I>n</I> and negative inertia <I>θ</I> (the number of negative eigenvalues): ∑ i = 1 k <SUB> λ i </SUB> ≤ n 2 ( θ + 1 ) ( θ + θ ( k θ + k − 1 ) ) with equality holding if and only if G ≅ n <SUB> K 1 </SUB> or G ≅ <SUB> p K ‾ t </SUB> ( n = p t , p ≥ 2 ) with k = 1 (where <SUB> p K ‾ t </SUB> is the complete <I>p</I>-partite graph of <I>p</I> <I>t</I> vertices with all partition sets having size <I>t</I>). Moreover, we obtain a sharp upper bound on the energy of bipartite graphs with given order <I>n</I> and rank <I>r</I>. We also propose an open problem as follows:</P> <P>Characterize all connected <I>d</I>-regular bipartite graphs of order <I>n</I> with 5 distinct eigenvalues and rank r = 2 <SUP> n 2 </SUP> <SUP> ( 4 d − n ) 2 </SUP> , where d > n 4 .</P> <P>Finally we give a partial solution to this problem.</P>

Compressive and rarefactive dust ion-acoustic Korteweg–de Vries and modified Korteweg–de Vries solitons in a multi-component dusty plasma

Das Samiran,Das Dulal Chandra 한국물리학회 2023 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.83 No.4

Non-linear propagation of dust ion-acoustic (DIA) solitary waves in a multi-component plasma consisting of ions, Cairn’s distributed electrons and immobile dust has been investigated theoretically. Reductive Perturbation Technique (RPT) is used to derive Korteweg–de Vries (KdV) and modifed Korteweg–de Vries (mKdV) equations. Both compressive as well as rarefactive solitons (compressive in most of the situations) and only compressive mKdV solitons are found to exist for this plasma. Many interesting facts on amplitude as well as width of solitons are established by comparing KdV and mKdV solitons under the same set of diferent plasma parameters. The investigation is being done in two diferent modes and found that the non-thermal parameter (β) and the number of dust charge contained in a immobile dust particle (Zd) plays very important role in the formation of both KdV and mKdV solitons.

Propagation of higher-order compressive dust–ion acoustic solitary waves in a dusty plasma with weak relativistic electrons

Das Dulal Chandra,Das Samiran 한국물리학회 2024 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.84 No.3

Higher-order dust–ion acoustic solitary waves are investigated theoretically for a multicomponent relativistic dusty plasma consisting of nonthermal ions, weakly relativistic electrons and mobile dust particles through reductive perturbation technique by deriving modifed Korteweg–de Vries (mKdV) equation. Amplitudes of relativistic dust–ion acoustic solitary waves are investigated for diferent initial streaming speed of ions, weakly relativistic electrons and dust particles and found that there is non-existence region of soliton for some initial streaming of ions as well as electrons. Interestingly, relativistic electron has a region of critical initial streaming speed at which amplitudes of the solitons are equal for diferent initial streaming of ions whereas for diferent initial streaming of electrons, the amplitudes of solitons become same after a certain value of initial streaming of ions, which is a salient feature of this investigation. It is also found that the amplitudes of the relativistic dust–ion acoustic solitary waves increase concavely with the increase in dust charges for smaller values of initial streaming of dust particles, whereas the growth of the same is concave for higher initial streaming of dust particles. The width of the relativistic dust–ion acoustic solitary wave is also investigated for diferent initial streaming of plasma particles.

Statistically Convergent Fuzzy Sequence Spaces by Fuzzy Metric

Das, Paritosh Chandra Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.3

In this article we study different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like completeness, solidness, sequence algebra, symmetricity and convergence free.

Increasing Histone Acetylation of Cloned Embryos, But Not Donor Cells, by Sodium Butyrate Improves Their <i>In Vitro</i> Development in Pigs

Das, Ziban Chandra,Gupta, Mukesh Kumar,Uhm, Sang Jun,Lee, Hoon Taek Mary Ann Liebert 2010 Cellular reprogramming Vol.12 No.1

<P>Abstract Previous studies have demonstrated that increased histone acetylation in donor cells or cloned embryos, by applying a histone deacetylase inhibitor (HDACi) such as trichostatin A (TSA), significantly enhances their developmental competence. However, its effect may vary with the type of HDACi and the target species, with some research showing nonsignificant or detrimental effects of TSA on in vitro and in vivo development of embryos. In this study, we show that sodium salt of butyric acid, a short-chain fatty acid produced naturally in the body by bacterial degradation of dietary fibers in the colon and rectum, increases histone acetylation in pig fibroblast and embryos at a concentration of 1.0 and 5.0 mM, respectively. However, treatment of donor cells with NaBu did not affect the rate of blastocyst formation or embryo quality in terms of histone acetylation and total nuclei per blastocyst (p > 0.05). On the contrary, treatment of cloned pig embryos with NaBu for 4 h significantly enhanced (p < 0.01) the rate of blastocyst formation (18.3 +/- 2.1 vs. 11.2 +/- 3.0%), although the total nuclei number per blastocyst did not differ. More importantly, blastocysts generated from NaBu-treated cloned embryos had increased levels of histone acetylation that was comparable to those of in vitro fertilized (IVF) embryos (36.7 +/- 3.6 vs. 45.9 +/- 2.5). In conclusion, our data suggest that histone hyperacetylation by NaBu treatment of cloned embryos, but not donor cell, enhances their in vitro development up to blastocyst stage.</P>

Supplementation of insulin-transferrin-selenium to embryo culture medium improves the <i>in vitro</i> development of pig embryos

Das, Ziban Chandra,Gupta, Mukesh Kumar,Uhm, Sang Jun,Lee, Hoon Taek Cambridge University Press 2014 Zygote Vol.22 No.3

<B>Summary</B><P>Insulin, transferrin and selenium (ITS) supplementation to oocyte maturation medium improves the post-fertilization embryonic development in pigs. ITS is also commonly used as a supplement for the <I>in vitro</I> culture (IVC) of embryos and stem cells in several mammalian species. However, its use during IVC of pig embryos has not been explored. This study investigated the effect of ITS supplementation to IVC medium on the <I>in vitro</I> development ability of pig embryos produced by parthenogenetic activation (PA), <I>in vitro</I> fertilization (IVF) or somatic cell nuclear transfer (SCNT). We observed that ITS had no significant effect on the rate of first cleavage (<I>P</I> > 0.05). However, the rate of blastocyst formation in ITS-treated PA (45.3 ± 1.9 versus 27.1 ± 2.3%), IVF (31.6 ± 0.6 versus 23.5 ± 0.6%) and SCNT (17.6 ± 2.3 versus 10.7 ± 1.4%) embryos was significantly higher (<I>P</I> < 0.05) than those of non-treated controls. Culture of PA embryos in the presence of ITS also enhanced the expansion and hatching ability (29.1 ± 3.0 versus 18.2 ± 3.8%; <I>P</I> < 0.05) of blastocysts and increased the total number of cells per blastocyst (53 ± 2.5 versus 40.9 ± 2.6; <I>P</I> < 0.05). Furthermore, the beneficial effect of ITS on PA embryos was associated with significantly reduced level of intracellular reactive oxygen species (ROS) (20.0 ± 2.6 versus 46.9 ± 3.0). However, in contrast to PA embryos, ITS had no significant effect on the blastocyst quality of IVF and SCNT embryos (<I>P</I> > 0.05). Taken together, these data suggest that supplementation of ITS to the IVC medium exerts a beneficial but differential effect on pig embryos that varies with the method of embryo production <I>in vitro</I>.</P>

Role of Histone Acetylation on Development Potential of Cloned Porcine Embryos

Ziban Chandra Das,Su Young Han,Young Tae Heo,Hyun Seung Lee,Sang Jun uhm,Hoon Taek Lee 한국동물생명공학회(구 한국동물번식학회) 2007 Reproductive & developmental biology Vol.31 No.2

Comparison between open and closed methods of herniorrhaphy in calves affected with umbilical hernia

Bibek Chandra Sutradhar,Mohammad Farhad Hossain,Bhajan Chandra Das,김근형,Mohammad Alamgir Hossain 대한수의학회 2009 JOURNAL OF VETERINARY SCIENCE Vol.10 No.4

Umbilical hernias in calves commonly present to veterinary clinics, which are normally secondary to failure of the normal closure of the umbilical ring, and which result in the protrusion of abdominal contents into the overlying subcutis. The aim of this study was to compare the suitability of commonly-used herniorrhaphies for the treatment of reducible umbilical hernia in calves. Thirty-four clinical cases presenting to the Veterinary Teaching Hospital, Chittagong Veterinary and Animal Sciences University, Chittagong, Bangladesh from July 2004 to July 2007 were subjected to comprehensive study including history, classification of hernias, size of the hernial rings, presence of adhesion with the hernial sacs, postoperative care and follow-up. They were reducible, nonpainful and had no evidence of infection present on palpation. The results revealed a gender influence, with the incidence of umbilical hernia being higher in female calves than in males. Out of the 34 clinical cases, 14 were treated by open method of herniorrhaphy and 20 were treated by closed method. Complications of hernia were higher (21%) in open method-treated cases than in closed method-treated cases (5%). Hernia recurred in three calves treated with open herniorrhaphy within 2 weeks of the procedure, with swelling in situ and muscular weakness at the site of operation. Shorter operation time and excellent healing rate (80%) were found in calves treated with closed herniorrhaphy. These findings suggest that the closed herniorrhaphy is better than the commonly-used open method for the correction of reducible umbilical hernia in calves.

In Vitro Development of Frozen-killed Porcine Somatic Cells following Somatic Cell Nuclear Transfer

Ziban Chandra Das,Mukesh Kumar Gupta,Yoon Hee Jung,Su Young Han,Ji hoon Yang,Myung Rae Park,Sung Jun Uhm,Hoon Taek Lee 한국동물생명공학회(구 한국동물번식학회) 2008 발생공학 국제심포지엄 및 학술대회 Vol.2008 No.1

Successful and Efficient Lyophilization of Pig Sperm for Long-Term Storage

Ziban Chandra Das,Hye Ran Lee,Kyu Hee Choi,Mukesh Kumar Gupta,Hoon Taek Lee 한국동물생명공학회(구 한국동물번식학회) 2011 발생공학 국제심포지엄 및 학술대회 Vol.2011 No.1

Preservation of sperm is essential for long-term storage of valuable animal genetic resources and for the conservation of threatened mammalian species undergoing progressive extinction. In this study, using pig as a model system, we evaluated the feasibility of germ-plasm preservation via sperm cell lyophilization. We show that, pig sperm can be successfully lyophilized and stored in a liquid nitrogen-free condition for at least 6 months. Intracytoplasmic injection of lyophilized sperm (ICSI), stored at 4℃ for four months, into in vitro matured pig oocytes could successfully develop up to blastocyst stage (13.0±3.0%). Lyophilized sperm could also be stored at room temperature for at least three weeks without further compromising their in vitro development up to the blastocyst stage (14.6±3.2 vs. 16.6±5.1%; p>0.05). Blastocysts produced from ICSI of lyophilized sperm stored at 4℃ or room temperature contained similar number of cells per blastocyst (44.9±3.2 vs. 44.0±4.3; p>0.05) but was significantly lower than those produced from non-lyophilized fresh sperm (52.1±5.8 p>0.05). Interestingly, use of a custom-designed HEPES-buffered, calcium-free, defined medium for the lyophilization resulted in normal post-ICSI embryonic development up to blastula stage (23.4±2.8 vs. 24.0±2.9%) and, the resultant blastocysts contained similar number of cells per blastocyst (47.9±4.3 vs. 50.6±7.0) compared to those generated from non-lyophilized fresh sperm (p>0.05). These lyophilized sperm could also be stored at room temperature for at least three weeks with slight reduction in post-ICSI embryonic development (19.6±1.4%). Therefore, these results suggest that, pig sperm could be successfully and efficiently lyophilized for their long-term storage at 4℃. Lyophilization of sperm could be a practical option for long-term storage of mammalian germ-plasm.