Skew Pairs of Idempotents in Partial Transformation Semigroups

Let S be a regular semigroup. A pair (e,f) of idempotents of S is said to be a skew pair of idempotents if fe is idempotent, but ef is not. T. S. Blyth and M. H. Almeida (T. S. Blyth and M. H. Almeida, skew pair of idempotents in transformation semigroups, Acta Math. Sin. (English Series), 22 (2006), 1705–1714) gave a characterization of four types of skew pairs—those that are strong, left regular, right regular, and discrete—existing in a full transformation semigroup T(X). In this paper, we do in this line for partial transformation semigroups.

Interleukin-7 receptor α mutational activation can initiate precursor B-cell acute lymphoblastic leukemia

Interleukin-7 receptor α (encoded by IL7R) is essential for lymphoid development. Whether acute lymphoblastic leukemia (ALL)-related IL7R gain-of-function mutations can trigger leukemogenesis remains unclear. Here, we demonstrate that lymphoid-restricted mutant IL7R, expressed at physiological levels in conditional knock-in mice, establishes a pre-leukemic stage in which B-cell precursors display self-renewal ability, initiating leukemia resembling PAX5 P80R or Ph-like human B-ALL. Full transformation associates with transcriptional upregulation of oncogenes such as Myc or Bcl2, downregulation of tumor suppressors such as Ikzf1 or Arid2, and major IL-7R signaling upregulation (involving JAK/STAT5 and PI3K/mTOR), required for leukemia cell viability. Accordingly, maximal signaling drives full penetrance and early leukemia onset in homozygous IL7R mutant animals. Notably, we identify 2 transcriptional subgroups in mouse and human Ph-like ALL, and show that dactolisib and sphingosine-kinase inhibitors are potential treatment avenues for IL-7R-related cases. Our model, a resource to explore the pathophysiology and therapeutic vulnerabilities of B-ALL, demonstrates that IL7R can initiate this malignancy.

On the Monoid of Unital Endomorphisms of a Boolean Ring

Let X be a nonempty set and P(X) the power set of X. The aim of this paper is to provide an explicit description of the monoid End1P(X)(P(X)) of unital ring endomorphisms of the Boolean ring P(X) and the automorphism group Aut(P(X)) when X is finite. Among other facts, it is shown that if X has cardinality n≥1, then End1P(X)(P(X))≅Tnop, where Tn is the full transformation monoid on the set X and Aut(P(X))≅Sn.

Kakawin Kumudawati: Analisis Intertektualitas

<p>Kakawin Kumudawati narratively contains Tantri stories. Tantri as a treasure that is very popular in Bali so it is not surprising that Tantri continues to be transformed into various forms of literary genres. Kakawin Kumudawati tells one of the part of stories in the Tantri story, namely the “<em>angsa</em>” and “<em>empas</em>”. Kakawin Kumudawati is a unique work in terms of narrative content, which is built on characters who are husband and wife. Tantri texts have been copied into various literary genres. It is very interesting to study mainly from the source of story writing, so tracking the hypogram is very necessary. Intertextual provides an illustration that the text is present through the reading of other texts both as a mosaic trail and full transformation.</p><p>Kakawin Kumudawati's primary hypogram is Tantri Carita. The matrix that is determined is manah “mind” which builds the satya model of 'loyalty' which is translated as Panca Satya. In intertextual comparison, Kakawin Kumudawati fulfills three main concepts (1) expansion, (2) conversion, and (2) expression, while (3) modification is not found in Kakawin Kumudawati.</p>

Centralising Monoids with Low-Arity Witnesses on a Four-Element Set

As part of a project to identify all maximal centralising monoids on a four-element set, we determine all centralising monoids witnessed by unary or by idempotent binary operations on a four-element set. Moreover, we show that every centralising monoid on a set with at least four elements witnessed by the Maľcev operation of a Boolean group operation is always a maximal centralising monoid, i.e., a co-atom below the full transformation monoid. On the other hand, we also prove that centralising monoids witnessed by certain types of permutations or retractive operations can never be maximal.

Structure of principal one-sided ideals

We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as semigroups of transformations with restricted range or kernel.

On automorphisms of monotone transformation posemigroups

In this paper, we provide a simple generalization of results of Sullivan for [Formula: see text] the full transformation monotone pomonoid and for [Formula: see text] the partial transformation monotone pomonoid by showing that every automorphism of [Formula: see text] and [Formula: see text] is inner induced by the elements of [Formula: see text] the pogroup of all ordered bijections on [Formula: see text]. We also show that [Formula: see text] is isomorphic to [Formula: see text]. Finally, we apply these results to get some more results in this direction.

Semigroups of Terms, Tree Languages, Menger Algebra of n-Ary Functions and Their Embedding Theorems

The concepts of terms and tree languages are significant tools for the development of research works in both universal algebra and theoretical computer science. In this paper, we establish a strong connection between semigroups of terms and tree languages, which provides the tools for studying monomorphisms between terms and generalized hypersubstitutions. A novel concept of a seminearring of non-deterministic generalized hypersubstitutions is introduced and some interesting properties among subsets of its are provided. Furthermore, we prove that there are monomorphisms from the power diagonal semigroup of tree languages and the monoid of generalized hypersubstitutions to the power diagonal semigroup of non-deterministic generalized hypersubstitutions and the monoid of non-deterministic generalized hypersubstitutions, respectively. Finally, the representation of terms using the theory of n-ary functions is defined. We then present the Cayley’s theorem for Menger algebra of terms, which allows us to provide a concrete example via full transformation semigroups.

Creating Cross-Sector Partnerships

Chapter 9 examines the creation of cross-sector partnerships. These partnerships involve building unconventional relations between organizations that have traditionally not worked closely together, in particular between businesses and non-profit organizations. To achieve this, the different objectives and participating organizations need to be acknowledged and reflected in appropriate key performance indicators. Cross-sector partnerships go through several stages of development that move from philanthropy to transactions in the form of reciprocal exchanges between the partners, integration of the values and objectives of the partners, and transformation of these into values at the societal or community rather than the individual partner level. Completing the process of a full transformation of the partnership takes time and requires a sufficiently long-horizon on the part of the partner organizations.