## Publications

### Publication Type: Journal Article

Year of Publication Publication Type Title

2018

Journal Article

Dr. Sreeja V. K., “Unit Regular Inverse Monoids and Clifford Monoids (UAE)”, International journal of Engineering and Technology, vol. 7, no. 2.13, pp. 306-308, 2018.[Abstract]

Let S be a unit regular semigroup with group of units G = G(S) and semilattice of idempotents E = E(S). Then for every there is a such that Then both xu and ux are idempotents and we can write or .Thus every element of a unit regular inverse monoid is a product of a group element and an idempotent. It is evident that every L-class and every R-class contains exactly one idempotent where L and R are two of Greens relations. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. A completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. A Clifford semigroup is a completely regular inverse semigroup. Characterization of unit regular inverse monoids in terms of the group of units and the semilattice of idempotents is a problem often attempted and in this direction we have studied the structure of unit regular inverse monoids and Clifford monoids. More »»

2016

Journal Article

Dr. Sreeja V. K., “Characterization of Some Unit Regular Orthodox Submonoids of the Full Transformation Semigroup T(X)”, Southeast Asian Bulletin of Mathematics, vol. 40, no. 1, pp. 125-129, 2016.[Abstract]

. A unit regular monoid S is said to be R− strongly unit regular if for any x, y ∈ S, xRy (where R is the Green’s relation) implies that there exists an element u in the group of units of S such that x = yu. The full transformation semigroup T (X) on a finite set X is seen to be R-strongly unit regular [4]. Hence the unit regular orthodox monoid ML exist for T (X) [10]. Let G(X) denote the group of units of T (X). For a L− class L of T (X), TL is defined to be TL = ∪e∈E(L)He which is the union of the group H− classes (where E(L) denote the set of idempotents of the L− class L). Also GL is a maximal subgroup of G(X) making TL ∪ GL an unit regular orthodox monoid and ML is defined to be TL ∪ GL [10]. Here we characterize the unit regular orthodox monoid ML of T (X). In the case of T (X) we also identify the minimal subgroup G1L of G(X) which makes TL ∪ G1L an unit regular orthodox monoid. More »»

2015

Journal Article

Dr. Sreeja V. K. and A.R., R., “Some combinatorial results on the full transformation semigroup”, Southeast Asian Bulletin of Mathematics, vol. 39 , no. 4, pp. 583-593, 2015.

2015

Journal Article

Dr. Sreeja V. K., “Orthodox Unit Regular Submonoids of the Full Transformation Semigroup T(X)”, Southeast Asian Bulletin of Mathematics, vol. 39, pp. 711 - 715, 2015.[Abstract]

A unit regular monoid S is said to be R-strongly unit regular if for any x, y ∊ S, xRy (where R is the Green's relation implies that there exists an element u in the group of units G of S such that x = yu. The full transformation semigroup T (X) on a finite set X is seen to be R-strongly unit regular [11]. Hence the unit regular orthodox monoid QR exists for T (X) [10]. Let G(X) denote the group of units of T (X). For an R-class R of a R-strongly unit regular monoid S, ZR is defined to be ∪e∊E(R)(HG)e, where E(R) denote the set of idempotents in the R-class R and (HG)e denote the HG class containing e. (Here the equivalence HG is defined on the monoid S as xHGy if and only if x = yu and x = u'y for some unit u, u' in G.) Then QR = ZR ∪G'R (See the Remark after Theorem 1.2) is an unit regular orthodox submonoid of S. Here we characterize the unit regular orthodox monoid QR of T (X). [ABSTRACT FROM AUTHOR]

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2015

Journal Article

Dr. Sreeja V. K. and Rajan, A. R., “Some Properties of Regular Monoids”, Southeast Asian Bulletin of Mathematics, vol. 39, pp. 891 - 902, 2015.[Abstract]

A monoid S with group of units G is said to be regular if for each x ∈ S, there is an element a ∈ S such that x = xax. We consider arbitrary monoids and describe various properties depending on the group of units. Properties of regular monoids and description of some special classes of regular monoids are also given. [ABSTRACT FROM AUTHOR]

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2014

Journal Article

Dr. Sreeja V. K., “Some Maximal Bands of the Full Transformation Semigroup”, Southeast Asian Bulletin of Mathematics, vol. 38, no. 3, pp. 445-449, 2014.[Abstract]

Bands with identity are unit regular semigroups. Moreover in a unit regular semigroup the trivial group is necessarily a band with unity. We now describe some maximal unit regular subsemigroups of the full transformation semigroup T(X) whose group of units is {1}. They are maximal subbands of T(X).

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2014

Journal Article

Dr. Sreeja V. K. and Rajan, A. R., “Construction of Certain Unit Regular Orthodox Submonoids”, Southeast Asian Bulletin of Mathematics, vol. 38, no. 6, pp. 907–916, 2014.[Abstract]

A regular semigroup S is said to bo orthodox if for any e, f ∈ E(S), ef ∈ E(S) where E(S) denotes the set of idempotents of S. A regular monoid S is said to be unit regular if for any x ∈ S, there exists an element u in the group of units of S such that x = xux. Here we characterize some orthodox unit regular submonoids associated with the L−class and R− class of a R−strongly (L−strongly) unit regular monoid.

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2013

Journal Article

Dr. Sreekanth K. M., Fan, J., Biswas, A., Rao, G. M., Sreelatha, K. S., Belova, L., and K Rao, V., “A comparative study of room temperature ferromagnetism in MgO films deposited by rf/dc sputtering using high purity Mg and MgO targets”, Materials Express, vol. 3, pp. 328–334, 2013.[Abstract]

Thin films of nanocrystalline MgO were deposited on glass/Si substrates by rf/dc sputtering from metallic Mg, and ceramic MgO targets. The purpose of this study is to identify the differences in the properties, magnetic in particular, of MgO films obtained on sputter deposition from 99.99% pure metallic Mg target in a controlled Nitrogen + Oxygen partial pressure (O(2)pp)] atmosphere as against those deposited using an equally pure ceramic MgO target in argon + identical oxygen ambience conditions while maintaining the same total pressure in the chamber in both cases. Characterization of the films was carried out by X-ray diffraction, focussed ion beam cross sectioning, atomic force microscopy and SQUID-magnetometry. The `as-obtained' films from pure Mg target are found to be predominantly X-ray amorphous, while the ceramic MgO target gives crystalline films, (002) oriented with respect to the film plane. The films consisted of nano-crystalline grains of size in the range of about 0.4 to 4.15 nm with the films from metallic target being more homogeneous and consisting of mostly subnanometer grains. Both the types of films are found to be ferromagnetic to much above room temperature. We observe unusually high maximum saturation magnetization (MS) values of 13.75 emu/g and similar to 4.2 emu/g, respectively for the MgO films prepared from Mg, and MgO targets. The origin of magnetism in MgO films is attributed to Mg vacancy (V-Mg), and 2p holes localized on oxygen sites. The role of nitrogen in enhancing the magnetic moments is also discussed.

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2013

Journal Article

Dr. Sreeja V. K. and Rajan, A. R., “The partial strong unit regularity of the full transformation semigroup”, Southeast Asian Bulletin of Mathematics, vol. 37, no. 3, pp. 405-412, 2013.

2012

Journal Article

A. Pa Santhakumaran and Chandran, S. VbUllas, “The detour hull number of a graph”, Algebra and Discrete Mathematics, vol. 14, pp. 307-322, 2012.[Abstract]

For vertices u and v in a connected graph G = (V,E), the set ID[u,v] consists of all those vertices lying on a u - v longest path in G. Given a set S of vertices of G, the union of all sets ID [u,v] for u,v ∈ S, is denoted by ID [S]. A set S is a detour convex set if ID [S] = S. The detour convex hull [S] D of S in G is the smallest detour convex set containing S. The detour hull number dh(G) is the minimum cardinality among the subsets S of V with [S] D= V. A set S of vertices is called a detour set if ID [S] = V. The minimum cardinality of a detour set is the detour number dn(G) of G. A vertex x in G is a detour extreme vertex if it is an initial or terminal vertex of any detour containing x. Certain general properties of these concepts are studied. It is shown that for each pair of positive integers r and s, there is a connected graph G with r detour extreme vertices, each of degree s. Also, it is proved that every two integers a and b with 2 ≤ a ≤ b are realizable as the detour hull number and the detour number respectively, of some graph. For each triple D,k and n of positive integers with 2 ≤ k ≤ n - D + 1 and D ≥ 2, there is a connected graph of order n, detour diameter D and detour hull number k. Bounds for the detour hull number of a graph are obtained. It is proved that dn(G) = dh(G) for a connected graph G with detour diameter at most 4. Also, it is proved that for positive integers a,b and k ≥ 2 with a &lt; b ≤ 2a, there exists a connected graph G with detour radius a, detour diameter b and detour hull number k. Graphs G for which dh(G) = n - 1 or dh(G) = n - 2 are characterized. © Journal "Algebra and Discrete Mathematics".

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2012

Journal Article

Dr. Ravichandran J., “A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners”, Statistical Papers, vol. 53, pp. 531-547, 2012.[Abstract]

Ever since Professor Bancroft developed inference procedures using preliminary tests there has been a lot of research in this area by various authors across the world. This could be evidenced from two papers that widely reviewed the publications on preliminary test-based statistical methods. The use of preliminary tests in solving doubts arising over the model parameters has gained momentum as it has proven to be effective and powerful over to that of classical methods. Unfortunately, there has been a downward trend in research related to preliminary tests as it could be seen from only few recent publications. Obviously, the benefits of preliminary test-based statistical methods did not reach Six Sigma practitioners as the concept of Six Sigma just took off and it was in a premature state. In this paper, efforts have been made to present a review of the publications on the preliminary test-based statistical methods. Though studies on preliminary test-based methods have been done in various areas of statistics such as theory of estimation, hypothesis testing, analysis of variance, regression analysis, reliability, to mention a few, only few important methods are presented here for the benefit of readers, particularly Six Sigma quality practitioners, to understand the concept. In this regard, the define, measure, analyze, improve and control methodology of six sigma is presented with a link of analyze phase to preliminary test-based statistical methods. Examples are also given to illustrate the procedures. © 2010 Springer-Verlag.

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2012

Journal Article

A. Pa Santhakumaran and Chandran, S. VbUllas, “The vertex detour hull number of a graph”, Discussiones Mathematicae - Graph Theory, vol. 32, pp. 321-330, 2012.[Abstract]

For vertices x and y in a connected graph G, the detour distance D(x, y) is the length of a longest x-y path in G. An x - y path of length D(x, y) is an x - y detour. The closed detour interval I D[x, y] consists of x, y, and all vertices lying on some x-y detour of G; while for S ⊆ V(G), I D[S] = ∪ x,y∈S I D [x, y]. A set S of vertices is a detour convex set if I D [S] = S. The detour convex hull [S] D is the smallest detour convex set containing S. The detour hull number dh(G) is the minimum cardinality among subsets S of V(G) with [S] D = V(G). Let x be any vertex in a connected graph G. For a vertex y in G, denoted by I D[y] x, the set of all vertices distinct from x that lie on some x-y detour of G; while for S ⊆ V(G), I D[S] x = ∪ y∈S I D[y] x. For x ∉ S, S is an x-detour convex set if I D[S] x = S. The x-detour convex hull of S, [S] x D is the smallest x-detour convex set containing S. A set S is an x-detour hull set if [S] D x = V(G) - {x} and the minimum cardinality of x-detour hull sets is the x-detour hull number dh x(G) of G. For x ∉ S, S is an x-detour set of G if I D [S] x = V(G) - {x} and the minimum cardinality of x-detour sets is the x-detour number d x(G) of G. Certain general properties of the x-detour hull number of a graph are studied. It is shown that for each pair of positive integers a, b with 2 ≤ a ≤ b + 1, there exist a connected graph G and a vertex x such that dh(G) = a and dh x(G) = b. It is proved that every two integers a and b with 1 ≤ a ≤ b, are realizable as the xdetour hull number and the x-detour number respectively. Also, it is shown that for integers a, b and n with 1 ≤ a ≤ n - b and b ≥ 3, there exist a connected graph G of order n and a vertex x such that dh x(G) = a and the detour eccentricity of x, e D(x) = b. We determine bounds for dh x(G) and characterize graphs G which realize these bounds.

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2007

Journal Article

Dr. Usha Kumari P. V., “On (s, S) inventory system with random lead time and repeated demands”, International Journal of Stochastic Analysis, vol. 2006, 2007.

2005

Journal Article

Dr. Usha Kumari P. V., “On the queueing system Mn x /GD/ α”, Bull. Of Pure and Applied Sciences, vol. 14E, no. 2, pp. 115-125, 2005.

2004

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “ k-out-of- n system with repair: the max ( N, T) policy”, Performance Evaluation, vol. 57, pp. 221–234, 2004.

2004

Journal Article

A. R. Rjan and Dr. Sreeja V. K., “Description and Counting of the Sandwich Sets in Transformation Semigroups.”, Southeast Asian Bulletin of Mathematics, vol. 27, p. 907, 2004.

2002

Journal Article

A. Krishnamoorthy and Dr. Usha Kumari P. V., “GI/M/1/1 queue with finite retrials and finite orbits”, 2002.

2002

Journal Article

A. Krishnamoorthy, Dr. Usha Kumari P. V., and Lakshmy, B., “k-out-of-n-system with repair: The N-policy”, Asia Pacific Journal of Operational Research, vol. 19, pp. 47–62, 2002.

2001

Journal Article

A. Krishnamoorthy and Dr. Usha Kumari P. V., “ k-out-of- n: G system with repair: the D-policy”, Computers & Operations Research, vol. 28, pp. 973–981, 2001.

2001

Journal Article

S. R. Chakravarthy, Krishnamoorthy, A., and Dr. Usha Kumari P. V., “A k-out-of-n reliability system with an unreliable server and phase type repairs and services: the (N, T) policy”, International Journal of Stochastic Analysis, vol. 14, pp. 361–380, 2001.

2000

Journal Article

A. Krishnamoorthy and Dr. Usha Kumari P. V., “A queueing system with single arrival bulk service and single departure”, Mathematical and computer modelling, vol. 31, pp. 99–108, 2000.

2000

Journal Article

A. Krishnamoorthy and Dr. Usha Kumari P. V., “Queues with customers requiring random number of servers”, IAPQR TRANSACTIONS, vol. 25, pp. 97–106, 2000.

1999

Journal Article

A. Krishnamoorthy and Dr. Usha Kumari P. V., “Reliability of ak-out-of-n system with repair and retrial of failed units”, Top, vol. 7, pp. 293–304, 1999.

1998

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On a bulk arrival bulk service infinite service queue”, Stochastic analysis and applications, vol. 16, pp. 585–595, 1998.

1998

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy*, A., “On the queueing system”, Optimization, vol. 43, pp. 157–168, 1998.

1998

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “The queueing system M/MX (R)/infinity”, ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, vol. 15, pp. 17–28, 1998.

1998

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the queueing system GID xn/G/α with Markov dependent batch arrivals”, Opsearch, vol. 35, pp. 1-12, 1998.

1996

Journal Article

A. Krishnamoorthy and Dr. Usha Kumari P. V., “On some infinite server queues in discrete time”, International journal of information and management sciences, vol. 7, pp. 71–78, 1996.

1995

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “The queueing system BDG D∞∗∗”, Optimization, vol. 34, pp. 185–193, 1995.

1995

Journal Article

Dr. Usha Kumari P. V., Krishnamoorthy, A., and Kashyap, B. R. K., “On GIX (u)/G/∞ queue”, International journal of information and management sciences, vol. 6, pp. 59–67, 1995.

1994

Journal Article

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On an Infinite Server Queue”, OPSEARCH-NEW DELHI-, vol. 31, pp. 240–240, 1994.

### Publication Type: Conference Paper

Year of Publication Publication Type Title

2014

Conference Paper

Dr. Usha Kumari P. V., “A retrial Inventory system with an unreliable server”, in International Conference on Operational Research, Sri Venkateswara University,Tirupati, A.P, 2014.

2014

Conference Paper

T. P. Srinivas and .R.Manjusha, M., “A Novel Method For Vechicle And Speed Estimation In Aerial Images”, in International Conference on Signal and Speech Processing, TKM College of Engineering, Kollam, Kerela, 2014.

2012

Conference Paper

, Achuthan, K., O., S. C., and Sharma, S. K., “Studies of the influence of MWCNTs and electrolytes in Dye Sensitized solar cells”, in Proceedings published by ICMST, 2012.

2000

Conference Paper

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “Single arrival bulk service single departure queue”, in The Int. Conference on Stochastic processes and their applications, Anna University, Madras, 2000.

1998

Conference Paper

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “k-out-of-n system with general repair, The N–policy”, in Proc. II International symposium on Semi-Markov processes and their applications, Compiegne, France, Dec, 1998.

1995

Conference Paper

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the queueing system MD/GD/ α”, in International conference on Stochastic process and computer applications., PSG College of Technology, Coimbatore, 1995.

1994

Conference Paper

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the GIX(u) /G/ α queue”, in 3rd Ramanujam Symp. On Stochastic Processes and their Applications, Ramamijan institute, Madras, 1994.

1994

Conference Paper

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On an infinite server queue in discrete time”, in 3rd Ramanujam symp. On stochastic processes and their applications, Ramanujan instituterMadras, 1994.

### Publication Type: Conference Proceedings

Year of Publication Publication Type Title

2014

Conference Proceedings

M. R., “Metric Dimension of Special Graphs and its Isomorphism”, Annual Conference of Kerala Mathematical Association . 2014.

2008

Conference Proceedings

Dr. Usha Kumari P. V., “ Threshold Based Data Aggregation Algorithm to Detect Rainfall in land Slide”, international Conference on Wireless Networks, vol. 1. pp. 255-261, 2008.[Abstract]

Landslides are one of the environmental disasters that cause massive destruction of human life and infrastructure. Real time monitoring of a landslide prone areas are necessary to issue fore warning. To accomplish real time monitoring, massive amount of data have to be collected and analyzed within a short span of time. This work has developed a method for effective data collection and aggregation by implementing threshold alert levels. The sampling rates of threshold alert levels will determine amount of data collected and aggregated which will reduce the power consumption by each wireless sensor nodes. This work also helps to determine the appropriate sampling rates for each threshold level, and the expected number of data packets in the queue. The time delay in receiving the data packet at the analysis station can be determined by using the value of expected number of data packets in the queue.

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