Congruence Is Not Cosmetic

The Congruence Variety of Metaabelian Groups Is Not Self–dual

A lattice identity is given such that it holds but its dual fails in the normal subgroup lattices of metaabelian groups. Thus the congruence variety of metaabelian groups is not self-dual; this is the first example for a modular congruence variety which is not self-dual. For a ring R with unit element let L(R) denote the class of lattices embeddable in submodule lattices of R-modules. Then HL(R...

P-value: What is and what is not

The misinterpretation and misuse of p-value have been increasing for decades. In March 2016, the American Statistical Association released a statement to warn about the use and interpretation of p-value. In this study, we provided a definition and discussion of p-value and emphasized the importance of its accurate interpretation.    

Pectus Excavatum: Not Just a Cosmetic Concern

The exact cause of PEX is not known, but the primary theory centers around unbalanced overgrowth in the costochondral regions. One study showed that asymmetric PEX patients had shorter ribs on the more severely depressed side of the deformity. Up to 43% of PEX patients have a family history of the disease. It is thought to be a disease of multifactorial inheritance, and the exact genes implicat...

Congruence join semidistributivity is equivalent to a congruence identity

We show that a locally finite variety is congruence join semidistributive if and only if it satisfies a congruence identity that is strong enough to force join semidistributivity in any lattice.

Cosmetic dentistry is still dentistry.