‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

where Ω is a smooth bounded domain in R, 1 0, such that (M0) M(t) ≥ m0 for all t ≥ 0. f (x, t) : × R → R is a continuous function and satisfies the subcritical condition: ∣∣f (x, t)∣∣ ≤ C(|t|q−1 + 1), for some p < q ...

We show that extended cyclic codes over $$\mathbb {F}_q$$ with parameters $$[q+2,3,q]$$ , $$q=2^m$$ determine regular hyperovals. also $$[qt-q+t,3,qt-q]$$ $$1<t<q$$ q is a power of t, (cyclic) Denniston maximal arcs. Similarly, $$[q^2+1,4,q^2-q]$$ are equivalent to ovoid obtained from elliptic quadrics in PG(3, q). Finally, we give simple presentations arcs PG(2, q) and

When pumping from a single well in a real (heterogeneous) aquifer, the steady state drawdown at the well is proportional to the pumping rate through a value called the equivalent transmissivity, Tea, which, in short, is the value that best suits Thiem's formula. Equivalent transmissivity is not a local value, but some representative value of a certain area surrounding the well. By means of nume...

lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this‎ ‎paper‎. ‎for two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{t}_n^{p‎, ‎q}={t‎: ‎t$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. furthermore, ‎the last four trees‎, ‎in the $s$-order‎, ‎among $mathscr{t}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Consider a routing problem for a team of vehicles in the plane: target points appear randomly over time in a bounded environment and must be visited by one of the vehicles. It is desired to minimize the expected system time for the targets, i.e., the expected time elapsed betwe...

Let ut = $ u q(x)u :1⁄4 Lu in D · [0,1), where D R is a bounded domain with a smooth connected boundary S, and q(x) 2 L(S) is a real-valued function with compact support in D. Assume that u(x, 0) = 0, u = 0 on S1 S, u = a(s, t) on S2 = SnS1, where a(s, t) = 0 for t > T, a(s, t) 6 0, a 2 C([0,T];H(S2)) is arbitrary. Given the extra data uN jS2 1⁄4 bðs; tÞ, for each a 2 C ([0,T];H(S2)), where N i...

Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function π where for any two points p and q, π(p, q) is equal to the Euclidean length of the shortest path f...

Elastic modulus (shear modulus G or Young's modulus E) and internal friction Q-' were measured as a function of temperature on undoped Pb(Zr50Ti50)03, Pb(Zr,2Ti.,,)03 , Pb(Zr5,Ti,)0, ceramics from -180°C to 500°C. Experiments were performed at low and medium frequencies (0.1 Hz 4 kHz). The E(T) curves show two anomalies which are due to following phase transitions: tetragonal to cubic (Tc) and ...