The variational theory is an inextricable part of both continuum mechanics and physics, and plays an important role in mathematics and nonlinear science, however it is difficult to find a variational formulation for a nonlinear system, and it is more difficult for a fractional differential system. This paper is to search for a variational formulation for the Schrödinger-KdV system with M-fractional derivatives. The fractional complex transformation is used to convert the system into a traditional differential system, and the semi-inverse method is further applied to establish a needed variational principle.

The cellular architecture and histochemical nature of the enzyme secretory acinar cells of pancreas have been investigated in two species of fish, Labeo calbasu and Mystus gulio having different feeding habits. Histological analysis illustrates that the exocrine pancreatic tissues are scattered within the hepatic parenchyma as hepatopancreas and spleen as spleenpancreas in L. calbasu. The structural analysis also shows that exocrine as well as endocrine pancreatic tissues are also diffused in the adipose tissues in between the intestinal coiling of L. calbasu. In M. gulio the discrete pancreatic tissue is attached to the outer wall of the stomach and formed cluster of acini interspersed with small areas of islet of Langerhans and blood vessels. The exocrine pancreatic acinar cells are provided with conspicuous nuclei and densely packed acidophilic zymogen granules. The endocrine component of pancreas, islet of Langerhans is encircled by a thin connective tissue and comprised of α , β and δ cells. Different cell types in the islets are differentiated based mainly upon their shape, position, staining intensity and density of the cytoplasmic secretory granules. α cells contain sparse cytoplasm and densely stained nuclei, are generally located to the periphery of the islet. Aldehyde fuchsin positive β cells bear spherical nucleus and granular cytoplasm, are in the center of islet of Langerhans contacted with blood vessels. δ cells are few in number with light stained nuclei disperse in the pancreatic islet. Histochemical detection displays that the zymogen granules of exocrine acinar cells showing variegated intensities of tryptophan reaction, the precursor of numerous pancreatic enzymes which probably related to the food and feeding habits of the fishes concerned. The zymogen granules are larger in size and heavily deposited in the acinar cells of hepatopancreas of L. calbasu in comparison to M. gulio may be correlated with the herbivorous feeding habit in respect to secretion of digestive enzymes.

We elaborate a unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated conditions when the fundamental geometric objects (anchor, metric and linear connection, almost symplectic, and related almost complex structures) may be canonically defined by an N-connection induced from a regular Lagrangian (or Hamiltonian), in mechanical models, or by generic off-diagonal metric terms and nonholonomic frames, in gravity theories. Such geometric constructions are modelled on nonholonomic manifolds provided with nonintegrable distributions and related chains of exact sequences of submanifolds defining N-connections. We investigate the main properties of the Lagrange, Hamilton, Finsler-Riemann and Einstein-Cartan algebroids, construct and analyze exact solutions describing such objects.

The power graph P(G) of a finite group G is a graph whose vertex set is the group G and distinct elements x, y ∈,G are adjacent if one is a power of the other, that is, x and y are adjacent if x ∈,⟨, y⟩,or y ∈,⟨, x⟩, . In this paper, we study existence of the Hamilton cycle in the power graph of some finite nilpotent groups G with a cyclic subgroup as direct factor when G is written as direct product Sylow p-subgroups. For this purpose we use of cartesian product a spanning tree and a cycle. Finally, we determined values of n such that P(Un) is Hamiltonian, where Un is a group consist of all positive integers less than n and relatively prime to n under multiplication modulo n.