Review on Root System of Lie Superalgebras and Some Partial Results on Splints of A(m,n)

Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. This dissertation deals with the splints of the root systems of Classical Lie superalgebra which can be seen as a generalisation of a Lie algebra to include a Z2 − grading. The term ’Splints’ is first coined by David A Richter which play an important role in determining the branching rules of a module over a complex semisimple Lie algebra. These results have been extended to classical Lie superalgebras which gave interesting results with regards to the graded algebras

Preparation of low cost herbal mosquito repellent from Begunia leaf

Vitex negundo (Verbenaceae) is a hardy plant, flourishing mainly in the Indian subcontinent. All parts of the plant, from root to fruit, possess a multitude of phytochemical secondary metabolites which impart an unprecedented variety of medicinal uses to the plant. Lager trials are required to prove its all activities before it is recommended in future for clinical industry. It is interesting to note that a single plant species finds use for treatment of a wide spectrum of health disorders in traditional and folk medicine; some of which have been experimentally validated. The plant is a component of a number of commercially available herbal formulations and has also shown potential as an effective bio-control agent. Employment of techniques such as cell and tissue culture would provide means of rapid propagation and conservation of the plant species and from the point of view of phytochemistry, give scope for enhancement of the quality and quantity of the bioactive secondary metabolites occurring in the plant

On the dimension of non-abelian tensor square of Lie superalgebras

In this paper, we determine upper bound for the non-abelian tensor product of finite dimensional Lie superalgebra. More precisely, if $L$ is a non-abelian nilpotent Lie superalgebra of dimension $(k \mid l)$ and its derived subalgebra has dimension $(r \mid s)$, then $\dim (L\otimes L) \leq (k+l-(r+s))(k+l-1)+2$. We discuss the conditions when the equality holds for $r=1, s=0$ explicitly

Properties of Sequences and Sums Associated with Balancing-like Sequences

The balancing like sequences are natural generalizations of the balancing sequence with one exception that the balancing-like numbers do not arise out of any balancing problem. The balancing-like sequences also generalize the sequence of natural numbers and like the balancing numbers, they behave like natural numbers and in some identities. Also, in some identities, they behave like the trigonometric sine function. Certain recurrence sequences naturally arise in connection with the balancing sequence, namely, the Lucas-balancing sequence, the cobalancing sequence and the Lucas cobalancing sequence. Like the balancing numbers, the basic definition of cobalancing numbers involves a Diophantine equation comprising of natural numbers. However, the cobalancing numbers are nothing but the balancers–a type of numbers associated with the definition of balancing numbers. The Lucas-balancing numbers are related to the balancing numbers by means of a simple nonlinear relationship that leads to a Pell’s equation. The Lucas-cobalancing numbers appears with cobalancing numbers, exactly the way Lucas-balancing numbers appears with the balancing numbers. But, in some identities, the cobalancing, Lucas-balancing and Lucas-cobalancing numbers appear as linear combinations of the balancing numbers. Using similar linear relations, cobalancing-like and Lucas-cobalancing-like numbers are defined using a balancing-like sequence. The properties of these two new sequences are identical with that of the cobalancing and the Lucas-cobalancing msequences. The nth triangular number is defined as the sum of the first n natural numbers or the product of n and n + 1 divided by 2. The triangular numbers can be generalized to triangular-like numbers using a balancing-like sequence. The nth triangular-like number corresponding to a balancing-like sequence can be defined as the product of nth and (n+1)th term of the sequence divided by the second term. The nth triangular-like number, so defined, is not equal to the sum of first n terms of the corresponding balancing-like sequence, rather it is equal to the sum of first n terms of another balancing-like sequence. It is known that a natural number is a triangular number when eight times the number increased by 1, is a square. However, a natural number is a triangular-like number corresponding to a balancing-like sequence if two separate multiples of the numbers increased by 1, are perfect squares. A pronic number is the product of two consecutive natural numbers and a pronic-like number is defined as the product of any two consecutive terms of a balancing-like sequence. The balancing sequence is the only balancing-like sequence whose pronic-like numbers are both pronic and triangular and there are exactly two balancing-like sequences with triangular pronic-like numbers. Using the Fibonacci and Pell sequences, several balancing-like sequences can be constructed. Balancing-like sequences also appear in the products of some special Lucas sequences and their associated sequences

Evaluation of Salmonella enterica serovar Typhimurium TTSS-2 deficient fur mutant as safe live-attenuated vaccine candidate for immunocompromised mice.

Salmonella enterica serovar Typhimurium has been extensively exploited as live attenuated vaccines (LAV) which generally confers better protection than killed or subunit vaccines. However, many LAV are limited by their inherent ability to access systemic organs in many of the vaccinated hosts, especially those which are immunocompromised. We evaluated the efficacy of a live-attenuated SPI2-deficient (ΔssaV) S. Typhimurium vaccine candidate (MT13) that additionally devoids the ferric uptake regulator (fur). We used specific pathogen free (SPF) streptomycin-pretreated mouse colitis model that included healthy C57BL/6 and immunocompromised iNos(-/-), IL10(-/-) and CD40L(-/-) in the background of C57BL/6 mice to assess the efficacy of developed vaccine candidate. In our study, the S. Typhimurium MT13 strain was established as a safe vaccine candidate to be administered in immunocompromised mice as it was found to be systemically attenuated without conferring significant pathological signs and growth defect within the host. In bacterial challenge experiment, the MT13-vaccinated C57BL/6 mice were protected from subsequent wild-type S. Typhimurium infection by inducing proficient mucosal immunity. The MT13 strain elicited efficient O-antigen specific mucosal secretory IgA associated protective response which was comparable with its parental ssaV mutant. Vaccination with MT13 also showed proficient T-cell activation in host mice; which has direct relation with pathogen clearance from host tissues. Collectively, these data implicate the possible application of SPI-2 deficient fur mutant (MT13) as a novel live attenuated vaccine strain with adept immunogenicity and improved safety, even in immunocompromised hosts. Further, this vaccine candidate can be employed to express heterologous antigens targeted against several other diseases, especially related to enterocolitic pathogens

<i>S.</i> Typhimurium challenge experiment: an assessment of vaccination efficacy.

<p>Vaccinated C57BL/6 mice groups (PBS: n = 4, MT12: n = 4 and MT13: n = 4) were ampicillin-treated (25 mg by gavage), challenged with wild-type SB300 (amp^r, sm^r) and euthanized at day 3 post-challenge (p.c.) i.e. day 34 post-vaccination. <b>A:</b> Colonization at various host sites after SB300 challenge. <b>B:</b> Enumeration of cecal pathology in terms of 13 point pathoscore scale was determined as described above (see material and methods). Broken lines in the graphs shows minimum detection limit. n.s.: not significant, *: statistically significant (P<0.05, t-test). <b>C:</b> Representative HE-stained cecum sections obtained from SB300-challenged mice groups immunized with PBS, MT12, MT13. Bar, 200 µm. S, submucosal edema; Lp, lamina propria; L, lumen.</p

Colonisation of vaccine candidate and its systemic access.

<p>Vaccination-challenge experiment to analyze the immunogenic potential of <i>S.</i> Typhimurium M12 and MT13 strain. Groups of C57BL/6 mice were vaccinated with 5×10⁷ cfu of <i>Salmonella</i> Typhimurium MT12 (<i>ssaV</i> mutant; closed grey circles; n = 8) and MT13 (<i>ssaV</i> and <i>fur</i> double mutant; closed black circles; n = 8) by gavage. One group of mice was treated with PBS (open circles; n = 8) to serve as control. Mice groups were kept under observation for next 30 days. <b>A:</b> Fecal shedding of <i>Salmonella</i> strains as analyzed by plating at various time-points in days. Four mice from each vaccinated group were sacrificed at day 30 post-vaccination (p.v.) to assess the bacterial population at different host sites. <b>B:</b> Enumeration of bacterial loads at various host sites. Broken lines in the graphs shows minimum detection limit. n.s.: not significant, *: statistically significant (P<0.05, t-test).</p