The main objective of the present paper is to derive the integral representation, matrix recurrence relations and matrix differential recurrence relations for the generalized Bessel matrix polynomials. Furthermore, we obtain a class of generating matrix functions for the generalized Bessel matrix polynomials by using the representation of a Lie group theory with the aid of Weisner's method. Some particular cases of interest as well as the applications of our results are also presented out.

The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D2 are established.

The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D2 are established.

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The main aim of this present paper is to investigate a new of interesting generating matrix relation for Legendre matrix polynomials with the help of a Lie group-theoretic method. Certain properties are well known but some of them are believed to be novel families of matrix differential recurrence relations and generating matrix functions for these matrix polynomials. Special cases of new results are also
given here as applications.

Nonisothermal dehydration of un-irradiated
and γ-ray irradiated holmium acetate tetrahydrate with
103 kGy total γ-ray dose absorbed was studied in air
atmosphere. The thermal decomposition experiments
were conducted at heating rates of (5, 7.5 and 10 °C/min).
The results showed that for un-irradiated material,
the dehydration process proceeds in two decomposition
steps with the elimination of 3.0 and 1.0 moles of
H2O, respectively. The apparent activation energy, Ea,
as given by both linear and nonlinear isoconversional
methods showed dependence upon the conversion
degree, α, in the range of 0.2–0.75 for the two dehydration
steps. In the first dehydration step, the Ea decreases
from 228.0 kJ/mol at the beginning of the decomposition
to ≈64.0 kJ/mol at the end of the process. In the
second dehydration step, the Ea increases from 42.0 to
72.0 kJ/mol by progressively increasing in α. Compared
with solid state reaction models, the two reactions are
best described by diffusion (D4) and nucleation (A3)
models for the first and second dehydration steps,
respectively. The results derived from nonisothermal
data present a reliable prediction of isothermal kinetics.
Straight lines and reduced time plots methods were
applied for the determination of the kinetic triplet [Ea,
ln A, and reaction model f(α)] from predicted isothermal
data. For γ-ray irradiated samples of Ho(CH3COO)3⋅4H2O
with 103 kGy total absorbed dose, the dehydration proceeds
in two overlapped steps controlled by D3 model.
X-ray data showed phase transformation from monoclinic
(SG P2/m) to tetragonal phase (SG P4/mmm) by the elimination of water content from the entire structure
of Ho(CH3COO)3⋅4H2O. γ-Ray irradiation effects
on the thermal decomposition of Ho(CH3COO)3⋅4H2O
were evaluated and discussed based on the formation
of trapped electrons, point defects, cation and anion
vacancies and cluster imperfections in the host lattice of
Ho(CH3COO)3⋅4H2O.

Nonisothermal dehydration of un-irradiated
and γ-ray irradiated holmium acetate tetrahydrate with
103 kGy total γ-ray dose absorbed was studied in air
atmosphere. The thermal decomposition experiments
were conducted at heating rates of (5, 7.5 and 10 °C/min).
The results showed that for un-irradiated material,
the dehydration process proceeds in two decomposition
steps with the elimination of 3.0 and 1.0 moles of
H2O, respectively. The apparent activation energy, Ea,
as given by both linear and nonlinear isoconversional
methods showed dependence upon the conversion
degree, α, in the range of 0.2–0.75 for the two dehydration
steps. In the first dehydration step, the Ea decreases
from 228.0 kJ/mol at the beginning of the decomposition
to ≈64.0 kJ/mol at the end of the process. In the
second dehydration step, the Ea increases from 42.0 to
72.0 kJ/mol by progressively increasing in α. Compared
with solid state reaction models, the two reactions are
best described by diffusion (D4) and nucleation (A3)
models for the first and second dehydration steps,
respectively. The results derived from nonisothermal
data present a reliable prediction of isothermal kinetics.
Straight lines and reduced time plots methods were
applied for the determination of the kinetic triplet [Ea,
ln A, and reaction model f(α)] from predicted isothermal
data. For γ-ray irradiated samples of Ho(CH3COO)3⋅4H2O
with 103 kGy total absorbed dose, the dehydration proceeds
in two overlapped steps controlled by D3 model.
X-ray data showed phase transformation from monoclinic
(SG P2/m) to tetragonal phase (SG P4/mmm) by the elimination of water content from the entire structure
of Ho(CH3COO)3⋅4H2O. γ-Ray irradiation effects
on the thermal decomposition of Ho(CH3COO)3⋅4H2O
were evaluated and discussed based on the formation
of trapped electrons, point defects, cation and anion
vacancies and cluster imperfections in the host lattice of
Ho(CH3COO)3⋅4H2O.