# Journal of Prime Research in Mathematics

Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing two issues in June and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year.

Latest Published Articles

### On realizations of the steenrod algebras

JPRM-Vol. 1 (2006), Issue 1, pp. 101 – 112 Open Access Full-Text PDF
Alexei Lebedev, Dimitry Leites
Abstract: The Steenrod algebra can not be realized as an enveloping of any Lie superalgebra. We list several problems that suggest a need to modify the definition of the enveloping algebra, for example, to get rid of certain strange deformations which we qualify as an artifact of the inadequate definition of the enveloping algebra in positive characteristic. P. Deligne appended our paper with his comments, hints and open problems

### Effect of convection on wavelet estimation for a multidimensional acoustic earth

JPRM-Vol. 1 (2005), Issue 1, pp. 220 – 226 Open Access Full-Text PDF
Abstract: We extend the wavelet estimation method due to Weglein and Secrest [4] to a marine seismic exploration model by taking into account the fluid motion and obtain the wavelet amplitude of the reflected data. This consideration is important for processing marine seismic data and for modeling seismic response. In case of known source location, the method predicts the source spectrum whereas the wave-field is predicted when the source (discrete/continuously distributed) is completely unknown. Moreover, this method is independent of the information about the properties of the earth. We find that the wavelet amplitude tends to zero and as a result, the corresponding reflected waves will be suppressed when the speed of the moving fluid gets closer and closer to the speed of sound. When the speed of the fluid motion is minuscule in comparison with the wave speed in water (Mach number $$M << 1$$), it does not effect the wavelet amplitude and the fluid motion can altogether be ignored which is in accordance with the physical observation.

### Separation of variables for nonlinear wave equation in cylinder coordinates

JPRM-Vol. 1 (2005), Issue 1, pp. 206 – 2019 Open Access Full-Text PDF
Alexander Shermenev
Abstract: Some classical types of nonlinear wave motion in the cylinder coordinates are studied within quadratic approximation. When the cylinder coordinates are used, the usual perturbation techniques inevitably leads to over determined systems of linear algebraic equations for the unknown coefficients (in contrast with the Cartesian coordinates). However, we show that these over determined systems are compatible for the special case of the nonlinear acoustical wave equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear acoustical wave equation which are found with the same accuracy as the equation is derived.

### Some properties of fractional Ornstein-Uhlenbeck process

JPRM-Vol. 1 (2005), Issue 1, pp. 193 – 205 Open Access Full-Text PDF
S. C. Lim
Abstract: We study the solution of fractional Langevin equation at both zero and positive temperature. The partition function and other thermodynamic properties associated with the solution (or the fractional Ornstein-Uhlenbeck process) can be obtained by using the generalized zeta function and the heat kernel techniques.

### On the conversion of rational triangular Bézier surfaces and multi-sided patches

JPRM-Vol. 1 (2005), Issue 1, pp. 184 – 192 Open Access Full-Text PDF
Germain E. Randriambelosoa, Malik Zawwar Hussain
Abstract: By a convenient parameter change we give a necessary and sufficient condition for the
conversion of a degree $$n$$ rational triangular Bézier surfaces to a degree $$n × n$$ rectangular surface whose one of the four edges is reduced to a single multiple point. Using then the method of base point we obtain the explicit expression of multi-sided patches in Bézier form.

### Continuous automorphisms and an equivalence relation In $$K[[X]]$$

JPRM-Vol. 1 (2005), Issue 1, pp. 178 – 183 Open Access Full-Text PDF
Shaheen Nazir
Abstract: Let K be an arbitrary commutative field and let $$R = K[[X]]$$ be the ring of formal power series in one variable. Let $$G_{R}$$ be the set of all power series of the form $$u = Xv$$, where $$v$$ is a unity in $$R$$. Relative to the usual composition $$G_{R}$$ becomes a topological group with respect to the $$X-$$adic topology of $$R$$. We also study an equivalence relation on $$R$$. Let $$R = K[[X]]$$ be the ring of formal power series in one variable over a fixed commutative field $$K$$. We denote by $$ord f = min \{i: a_{i} ≠ 0\}$$ for any $$f ∈ R$$ . It is well known that $$ord f$$ is a valuation on $$R$$ and $$R$$ becomes a complete topological ring relative to the topology induced by this valuation. Let  $$G_{G}=\{u∈ R: ord u=1\}$$ and for $$u,v ∈ R_{G}$$ we denote $$(uov)(X)=v(u(X))$$, a new element of $$R_{G}$$.