Mal’tsev products of varieties, I

We investigate the Mal’tsev product $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W of two varieties $$\mathcal {V}$$ V and $$\mathcal {W}$$ W of the same similarity type. While such a product is usually a quasivariety, it is not necessarily a variety. We give an equational base for the variety generated by $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W in terms of identities satisfied in $$\mathcal {V}$$ V and $$\mathcal {W}$$ W . Then the main result provides a new sufficient condition for $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W to be a variety: If $$\mathcal {W}$$ W is an idempotent variety and there are terms f(x, y) and g(x, y) such that $$\mathcal {W}$$ W satisfies the identity $$f(x,y) = g(x,y)$$ f ( x , y ) = g ( x , y ) and $$\mathcal {V}$$ V satisfies the identities $$f(x,y) = x$$ f ( x , y ) = x and $$g(x,y) = y$$ g ( x , y ) = y , then $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W is a variety. We provide a number of examples and applications of this result.

KERAGAMAN JENIS HAMA KUTU PUTIH PADA TANAMAN SINGKONG DI KOTA ENDE

This study aims to determine the type of white lice (Mealybug) pest associated with cassava plants (ManihotesculentaCrantz) in Ende Regency. The observation variables used included the identification of the hamlet species found in the field and calculating the level of diversity, abundance, dominance, similarity / similarity and intensity of pest attacks. The results showed that the diversity index for Nangapanda District was 1.052 (medium), abundance of 0.243 (low), and dominance index of 0.465 (moderate). Ende District diversity index 0.953 (low), abundance 0.348 (low), and dominance index 0.428 (moderate). Ende Selatan Subdistrict diversity index is 0.927 (low), abundance is 0.351 (low), and dominance index is 0.438 (moderate). In NdonaSubdistrict the diversity index is 0.683 (low), abundance is 0.358 (low), and dominance is 0.397 (moderate). For the similarity / similarity type index between Nangapanda sub-district and other sub-districts which is 85.71%. Similarity / similarity between Ende District and three other Sub-districts, namely 85.71%, 100% and 100%. The similarity between Ende Selatan District and the other three Sub-districts is 85.71%, 100% and 100%. The similarity between NdonaSubdistrict and the other three Subdistricts is 85.71%, 100% and 100%. While the intensity of pest damage in each Subdistrict was 47.7%, in Ende District 32.5%, South Ende 25% and Ndona District 38.33%.

An integral relationship for a fractional one-phase Stefan problem

A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan (Fract. Calc. Appl. Anal., 16, No 4 (2013), 802–815) and Tarzia and Ceretani (Fract. Calc. Appl. Anal., 20, No 2 (2017), 399–421), because it allows us to work with Green’s identities (which does not apply when Caputo derivatives are considered). As a main result, an integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is also given.

One-Phase Stefan-Like Problems with Latent Heat Depending on the Position and Velocity of the Free Boundary and with Neumann or Robin Boundary Conditions at the Fixed Face

A one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions of similarity type are obtained for the cases when Neumann or Robin boundary conditions are imposed at the fixed face. Required relationships between data are presented in order that these problems become equivalent to the problem where a Dirichlet condition at the fixed face is considered. Moreover, in the case where a Robin condition is prescribed, the limit behaviour is studied when the heat transfer coefficient at the fixed face goes to infinity.

Boolean like algebras

Using Vaggione's concept of central element in a double pointed algebra, weintroduce the notion of Boolean like variety as a generalisation ofBoolean algebras to an arbitrary similarity type. Appropriately relaxing therequirement that every element be central in any member of the variety, weobtain the more general class of semi-Boolean like varieties, whichstill retain many of the pleasing properties of Boolean algebras. We provethat a double pointed variety is discriminator iff it is semi-Boolean like,idempotent, and 0-regular. This theorem yields a new Maltsev-stylecharacterisation of double pointed discriminator varieties.Moreover, we point out the exact relationship between semi-Boolean-likevarieties and the quasi-discriminator varieties, and we providesemi-Boolean-like algebras with an explicit weak Boolean productrepresentation with directly indecomposable factors. Finally, we discuss idempotentsemi-Boolean-like algebras. We consider a noncommutative generalisation of Boolean algebras and prove - along the lines of similar results available for pointed discriminator varieties or for varieties with a commutative ternary deduction term that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional operations.

TIPOLOGI BANGUNAN KOLONIAL BELANDA DI SINGARAJA

Architecture is component of a city. The presence of architecture, both traditional and colonial architecture has a historical and archaeological values and can be regarded as an identity of a city. Unfortunately modernization often leaves no place for a historical building that actually has an important role in the formation of characteristic of a place. Its result conflicts with "two side" between cultural heritage preservation activist with the destroyers of cultural heritage, which is the pick of capital. On the other hand, not least in the form of architectural heritage of Indo-European style building in Indonesia that offers various advantages in terms of engineering and the art of building. This paper objective is to identify the typology or the types of colonial architecture buildings in Singaraja and its characteristics. The method used is descriptive-analytical about the basic functions of grouping includes similarity type, form, structure and character of the building. Some of the existing architecture in Singaraja are Art Deco, Landhuis, and Gothic style. The typology of colonial buildings in Singaraja, are government buildings, homes, public building and others with a characteristic shape is relatively small, and very adaptive to the climate and natural conditions in Indonesia, especially Singaraja. Arsitektur merupakan salah satu komponen dari sebuah kota. Keberadaan arsitektur, baik arsitektur tradisional maupun kolonial memiliki nilai historis dan arkeologis dan dapat dianggap sebagai identitas suatu kota. Sayangnya modernisasi seringkali tidak menyisakan tempat untuk bangunan tua atau bersejarah yang sebenarnya memiliki peran penting dalam pembentukan karakteristik suatu tempat. Akibatnya terjadi konflik “dua kubu” antara pelestari warisan budaya dengan pihak perusak warisan budaya, terutama pemilik modal. Di lain pihak, tidak sedikit warisan arsitektural berupa bangunan bergaya indo-Eropa di Indonesia yang menawarkan berbagai keunggulan dalam hal teknik dan seni bangunan. Tujuan tulisan ini adalah untuk mengidentifikasi tipologi atau tipe-tipe bangunan-bangunan peninggalan kolonial di Singaraja beserta karakteristik arsitekturnya. Metode yang digunakan deskriptif-analitis tentang fungsi dasar pengelompokkan meliputi kesamaan tipe, bentuk, struktur dan karakter bangunan. Beberapa arsitektur yang ada di Singaraja antara lain gaya Art Deco, Landhuis, dan Gothic. Secara umum tipologi bangunan kolonial di Singaraja antara lain, gedung pemerintahan, rumah tinggal, sarana umum dan lain-lain dengan karakteristik bentuknya relatif kecil, dan sangat adaptif dengan iklim dan kondisi alam di Indonesia, khusunya Singaraja.