Let r ≥ 3 be integer, and let Gr denote the set of r-regular graphs with vertex set V = {1, 2, . . . , n}. Let G be chosen randomly from Gr. We prove that whp the cover time of a random walk on G is asymptotic to r−1 r−2 n log n.

In 1996, Fredman and Khachiyan [Journal of Algorithms, 21:618–628, 1996] presented a remarkable algorithm for the problem of checking the duality of a pair of monotone disjunctive normal forms. Their algorithm runs in no(log n) time, thus giving evidence that the problem lies in an intermediate class between P and co-NP. In this paper we show that a modified version of their algorithm requires ...

We construct closed immersions from initial degenerations of $${{\,\mathrm{Gr}\,}}_{0}(d,n)$$ —the open cell in the Grassmannian $${{\,\mathrm{Gr}\,}}(d,n)$$ given by nonvanishing all Plücker coordinates—to limits thin Schubert cells associated to diagrams induced face poset corresponding tropical linear space. These are isomorphisms when (d, n) equals (2, n), (3, 6) and 7). As an application w...

Abstract Finance is one of the promising field for industrial application quantum computing. In particular, algorithms calculation risk measures such as value at and conditional a credit portfolio have been proposed. this paper, we focus on another problem in management, contributions, which quantify concentration subgroups portfolio. Based recent algorithm simultaneous estimation multiple expe...

In the Junggar basin, northwest China, many high gamma-ray (GR) sandstone reservoirs are found and routinely interpreted as mudstone non-reservoirs, with negative implications for the exploration and exploitation of oil and gas. Then, the high GR sandstone reservoirs' recognition principles, genesis, and log evaluation techniques are systematically studied. Studies show that the sandstone reser...

Comment 1.i Determining the quantities used in the analysis: GR: -How much does the choice of the method for assessing GR (the log-normal fitting method) affect the obtained values? The maximum concentration method (see e.g. Kulmala et al., 2012) is also very often used; would the values change if this method was used instead? -Is GR corrected for coagulational losses, as proposed by Leppä et a...

This study was done to optimize accuracy of predicting growth of Salmonella serovars, Escherichia coli O157:H7, and Staphylococcus aureus in temperature-abused raw beef, poultry, and bratwurst (with salt but without added nitrite). Four mathematical approaches were used with experimentally determined lag-phase duration (LPD) and growth rate (GR) values to develop 12 versions of THERM (Temperatu...

Dalam mengembangkan lapangan produksi minyak dan gas, perlu dilakukan studi lingkungan pengendapan untuk dapat meningkatkan kualitas hasil produksi. Cekungan Jawa Timur Utara sebagian besar merupakan cekungan lepas pantai yang menghasilkan gas dengan shale Formasi Ngimbang sebagai batuan induk menggenerasikan hidrokarbon ke reservoir berupa karbonat (Formasi Kujung). Identifikasi menganalisa po...

The amplituhedron \(\mathcal{A}_{n,k,m}\) was introduced by Arkani-Hamed and Trnka (2014) in order to give a geometric basis for calculating scattering amplitudes planar \(\mathcal{N}=4\) supersymmetric Yang-Mills theory. It is projection inside the Grassmannian \(\text{Gr}_{k,k+m}\) of totally nonnegative part \(\text{Gr}_{k,n}\). Karp Williams (2019) studied \(m=1\) \(\mathcal{A}_{n,k,1}\), g...