Properties of the Upper and Lower Sequence on the Cage
نویسنده
چکیده
The terminology and notation used here are introduced in the following articles: [24], [27], [1], [3], [4], [2], [14], [12], [25], [22], [23], [11], [21], [8], [9], [6], [26], [15], [10], [18], [17], [5], [20], [19], [7], [13], and [16]. In this paper n is a natural number. We now state a number of propositions: (1) For all subsets A, B of E T such that A meets B holds proj1◦ A meets proj1◦ B. (2) Let A, B be subsets of E T and s be a real number. If A misses B and A ⊆ HorizontalLine s and B ⊆ HorizontalLine s, then proj1◦ A misses proj1◦ B. (3) For every closed subset S of E T such that S is Bounded holds proj1◦ S is closed. (4) For every compact subset S of E T holds proj1◦ S is compact. (5) Let p, q, p1, q1 be points of E 2 T . Suppose L(p, q) is vertical and L(p1, q1) is vertical and p1 = (p1)1 and p2 ¬ (p1)2 and (p1)2 ¬ (q1)2 and (q1)2 ¬ q2. Then L(p1, q1) ⊆ L(p, q). (6) Let p, q, p1, q1 be points of E 2 T . Suppose L(p, q) is horizontal and L(p1, q1) is horizontal and p2 = (p1)2 and p1 ¬ (p1)1 and (p1)1 ¬ (q1)1 and (q1)1 ¬ q1. Then L(p1, q1) ⊆ L(p, q). (7) Let G be a Go-board and i, j, k, j1, k1 be natural numbers. Suppose 1 ¬ i and i ¬ lenG and 1 ¬ j and j ¬ j1 and j1 ¬ k1 and k1 ¬ k and k ¬ widthG. Then L(G ◦ (i, j1), G ◦ (i, k1)) ⊆ L(G ◦ (i, j), G ◦ (i, k)).
منابع مشابه
On Moments of the Concomitants of Classic Record Values and Nonparametric Upper Bounds for the Mean under the Farlie-Gumbel-Morgenstern Model
In a sequence of random variables, record values are observations that exceed or fall below the current extreme value.Now consider a sequence of pairwise random variables {(Xi,Yi), i>=1}, when the experimenter is interested in studying just thesequence of records of the first component, the second component associated with a record value of the first one is termed the concomitant of that ...
متن کاملEntropy Properties of Certain Record Statistics and Some Characterization Results
In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...
متن کاملA Novel B and B Algorithm for a Unrelated Parallel Machine Scheduling Problem to Minimize the Total Weighted Tardiness
This paper presents a scheduling problem with unrelated parallel machines and sequencedependent setup times that minimizes the total weighted tardiness. A new branch-and-bound (B and B) algorithm is designed incorporating the lower and upper bounding schemes and several dominance properties. The lower and upper bounds are derived through an assignment problem and the composite dispatching rule ...
متن کاملHNO Detection by Nanosized B12N12 Cage: A DFT/TDDFT Study
The interaction of a nitrosyl hydride (HNO) molecule with B12N12 nanocage was explored by means of density functional calculations. It was found that HNO prefers to be adsorbing on a boron atom of the cage with adsorption energy of -0.65 eV. This adsorption process significantly shifts the HOMO-LUMO gap (Eg) of the cage to lower energies, thereby reducing Eg of the cage from 6.84 to 2.45 eV. Ti...
متن کاملOn the fine spectrum of generalized upper triangular double-band matrices $Delta^{uv}$ over the sequence spaces $c_o$ and $c$
The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007