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In this manuscript, the concept of ϝ-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of G-metric space, which is termed Jaggi-Suzukitype hybrid ϝ-(G-α-φ)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein. [ABSTRACT FROM AUTHOR]

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields of applied sciences. In the present article, a class of q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for a numerical solution of a distinct class of fractional differential inclusions have been achieved with the help of Schaefer type and Banach contraction fixed point theorems. A physical example is also provided to validate the hypothesis of the main results. The notion of q-rung orthopair fuzzy mappings along with the use of fixed point techniques and a new-fangled Caputo type fractional derivative are the principal novelty of this article. [ABSTRACT FROM AUTHOR]

A group G is said to be (l, m, n)-generated if it is a quotient of the triangle group T (l , m , n) = ⟨ x , y , z ∣ x l = y m = z n = x y z = 1 ⟩. Moori posed in 1993 the question of finding all the triples (l, m, n) such that non-abelian finite simple groups are (l, m, n)-generated. We partially answer this question for the Fischer sporadic simple group Fi23. In particular, we investigate all (2, q, r)-generations for the Fischer sporadic simple group Fi23, where q and r are distinct prime divisors of |Fi23|. [ABSTRACT FROM AUTHOR]

A group G is said to be (l, m, n)-generated if it is a quotient of the triangle group T (l , m , n) = ⟨ x , y , z ∣ x l = y m = z n = x y z = 1 ⟩. Moori posed in 1993 the question of finding all the triples (l, m, n) such that non-abelian finite simple groups are (l, m, n)-generated. We partially answer this question for the Fischer sporadic simple group Fi23. In particular, we investigate all (2, q, r)-generations for the Fischer sporadic simple group Fi23, where q and r are distinct prime divisors of |Fi23|. [ABSTRACT FROM AUTHOR]

A group G is said to be (l,m,n)-generated if it can be generated by two suitable elements x and y such that o(x) = l, o(y) = m and o(xy) = n. In [J. Moori, (p,q,r)-generations for the Janko groups J1 and J2, Nova J. Algebra Geom. 2 1993, 3, 277–285], J. Moori posed the problem of finding all triples of distinct primes (p,q,r) for which a finite non-abelian simple group is (p,q,r)-generated. In the present article, we partially answer this question for Fischer's largest sporadic simple group Fi′24 by determining all (3,q,r)-generations, where q and r are prime divisors of |Fi′24| with 3 < q < r. [ABSTRACT FROM AUTHOR]

A group G is said to be (l,m,n)-generated if it can be generated by two suitable elements x and y such that o(x) = l, o(y) = m and o(xy) = n. In [J. Moori, (p,q,r)-generations for the Janko groups J1 and J2, Nova J. Algebra Geom. 2 1993, 3, 277–285], J. Moori posed the problem of finding all triples of distinct primes (p,q,r) for which a finite non-abelian simple group is (p,q,r)-generated. In the present article, we partially answer this question for Fischer's largest sporadic simple group Fi′24 by determining all (3,q,r)-generations, where q and r are prime divisors of |Fi′24| with 3 < q < r. [ABSTRACT FROM AUTHOR]

If G is a finite group and X a conjugacy class of elements of G, then we define rank(G: X) to be the minimum number of elements of X generating G. In the present article, we determine the ranks for the Fischer's simple group Fi'24 and the baby monster group B. [ABSTRACT FROM AUTHOR]

A study was conducted under the laboratory conditions in the Department of Zoology, Wildlife and Fisheries, University of Agriculture, Faisalabad, Pakistan during 2014 to investigate the effect of supplementation of lysine on nutrient digestibility in the juveniles of Labeo rohita. Seven experimental diets were formulated by supplementing 0, 0.5, 1, 1.5, 2, 2.5 and 3% lysine and designated as D1, D2, D3, D4, D5, D6 and D7, respectively. To test each diet, two replicates with 20 fish each (average weight 3.526±0.056g) were assigned. The experiment was performed within the time duration of 60 days. Water quality parameters like dissolved oxygen (5.8-7.3 mg/L), temperature (24.9-28.7°C) and pH (7.4-8.6) were maintained throughout this period. Results showed that lysine supplementation in fish diet increased the digestibility of crude protein and dry matter. Maximum digestibility of crude protein and dry matter was observed at lysine level of 1.5 and 2.5%, respectively. However, it was observed that digestibility of crude fat decreased in response to lysine supplementation. In conclusion, it was found that lysine supplementation improved the nutrient digestibility performance of juveniles of L. rohita. [ABSTRACT FROM AUTHOR]