Weak core and central weak core inverse in a proper ∗*-ring

In this paper, we introduce the notion of weak core and central weak core inverse in a proper $*$-ring. We further elaborate on these two classes by producing a few representation and characterization of the weak core and central weak core invertible elements. We investigate additive properties and a few explicit expressions for these two classes of inverses through other generalized inverses. In addition to these, numerical examples are provided to validate a few claims on weak core and central weak core inverses.Comment: 20 pages, 1 figur

Online Subset Selection using α\alpha-Core with no Augmented Regret

We consider the problem of sequential sparse subset selections in an online learning setup. Assume that the set $[N]$ consists of $N$ distinct elements. On the $t^{\text{th}}$ round, a monotone reward function $f_t: 2^{[N]} \to \mathbb{R}_+,$ which assigns a non-negative reward to each subset of $[N],$ is revealed to a learner. The learner selects (perhaps randomly) a subset $S_t \subseteq [N]$ of $k$ elements before the reward function $f_t$ for that round is revealed $(k \leq N)$. As a consequence of its choice, the learner receives a reward of $f_t(S_t)$ on the $t^{\text{th}}$ round. The learner's goal is to design an online subset selection policy to maximize its expected cumulative reward accrued over a given time horizon. In this connection, we propose an online learning policy called SCore (Subset Selection with Core) that solves the problem for a large class of reward functions. The proposed SCore policy is based on a new concept of $\alpha$-Core, which is a generalization of the notion of Core from the cooperative game theory literature. We establish a learning guarantee for the SCore policy in terms of a new performance metric called $\alpha$-augmented regret. In this new metric, the power of the offline benchmark is suitably augmented compared to the online policy. We give several illustrative examples to show that a broad class of reward functions, including submodular, can be efficiently learned with the SCore policy. We also outline how the SCore policy can be used under a semi-bandit feedback model and conclude the paper with a number of open problems

Engineering properties of warm mix asphalt using synthetic zeolite as an additive

Warm mix asphalt(WMA) is a recent technology used to reduce the mixing and compactiontemperatures without affecting the quality of pavement. Warm mix asphalt is a bituminous mixture where all its constituents are mixed, placed, compacted at medium temperature .A number of WMA processes havebeen developed in recent days. One of the processes includes the use ofsynthetic zeolite as anadditive.An attempt has been made in the laboratory to develop warm mix asphalt mixes using synthetic zeolite asan additive at a specified mixing and compaction temperature which were obtained after a number of trials.Thestone matrix asphalt (SMA) and dense bituminous macadam (DBM)mixes with aggregate gradation as per MORTH specifications were made with varying bindercontents (5%,6% and7%). The zeolite content was 0.3% by weight of aggregate. Stone dust and cement were used as filler for SMA andDBM samples respectively. VG 30 grade bitumen was used as binder for both the mixes.Marshall procedure has been made for preparation of samples and evaluation of bituminous mixes. The volumetric properties (VA, VMA and VFB), stability, flow value and optimum binder content of the SMA and DBM mix samples have beeninvestigated. The optimum binder content ofthe DBM and SMA samples was found to be 5.3% and 5.8% respectively

The influence of gas hydrate morphology on reservoir permeability and geophysical shear wave remote sensing

We show that direct estimates of the permeability of hydrate-bearing geological formations are possible from remote measurements of shear wave velocity (Vs) and attenuation (Qs−1). We measured Vs, Qs−1 and electrical resistivity at time intervals during methane hydrate formation in Berea sandstone using a laboratory ultrasonic pulse-echo system. We observed that Vs and Qs−1 both increase with hydrate saturation Sh, with two peaks in Qs−1 at hydrate saturations of around 6% and 20% that correspond to changes in gradient of Vs. We implemented changes in permeability with hydrate saturation into well-known Biot-type poro-elastic models for two- and three-phases for low (Sh 12%) hydrate saturations respectively. By accounting for changes in permeability linked to hydrate morphology, the models were able to describe the Vs and Qs−1 observations. We found that the first Qs−1 peak is caused by a reduction of permeability during hydrate formation associated with a transition from pore-floating to pore-bridging hydrate morphology; similarly, the second Qs−1 peak is caused by a permeability reduction associated with a transition from pore-bridging hydrate morphology to an interlocking network of hydrate in the pores. We inverted for permeability using our poro-elastic models from Vs and Qs−1. This inverted permeability agrees with permeability obtained independently from electrical resistivity. We demonstrate a good match of our models to shear wave data at 200 Hz and 2 kHz frequencies from the literature, indicating the general applicability of the models

Study and Development of Handwritten Numeral Character Recognition

Image processing is basically used to extract useful information from any input image. Recognition has a very important role in image processing. In this exploration work, we have concentrated on the recognition of the handwritten numeral characters. Neural Network is used for recognizing the different handwritten numerals. Our method comprises of three stages and they are pre-processing, training and recognition. Pre-processing stages includes removal of noise, binarization, re-scaling and finding the skeleton of an image. Skew correction is also used for segmenting the different characters in an image. In training stage we have used back propagation technique for recognizing different numeral characters. Different hidden layers are used while training to have better accuracy. Recognition stage recognizes the different characters in an image from the trained neural network. The above proposed system has been performed in Matlab. The system detects the numerals with an exactness in around 90-95%.It works well and has the similar accuracy in even twisted pictures or pictures having different size