Zero Production Research Articles

Two-Sided Zero Product Determined Triangular Algebras

Two-Sided Zero Product Determined Triangular Algebras

Characterizations of derivations on incidence algebras by local actions

Let ( X , ≤ ) be a locally finite pre-ordered set and R be a commutative ring with unity. In this paper we apply the theory of zero product determined algebras to show that each linear map on the incidence algebra I ( X , R ) which is derivable at zero is a generalized derivation and every local derivation on I ( X , R ) is a derivation.

Lie centralizing mappings on generalized matrix algebras through two-sided zero products

Let [Formula: see text] be a generalized matrix algebra defined by the Morita context [Formula: see text] and [Formula: see text] the center of [Formula: see text]. In this paper, under some certain conditions on [Formula: see text], we prove that if [Formula: see text] is an additive map satisfying [Formula: see text] for any [Formula: see text] with [Formula: see text], then [Formula: see text] has the form [Formula: see text] for all [Formula: see text], where [Formula: see text] and [Formula: see text] is an additive map from [Formula: see text] into [Formula: see text]. Finally as its applications, we characterize Lie centralizer maps and generalized Lie derivations on [Formula: see text]. Moreover we prove that the similar conclusions remain valid on full matrix algebras, triangular algebras, upper triangular matrix algebras.

A finite-dimensional singular superalgebra is algebraically generated

This article is the final one in the series of papers by the authors devoted to finite-dimensional singular (simple right-alternative with zero product in the even part) superalgebras. In previous papers, algebraically generated singular superalgebras were studied and it was proved that any such superalgebra has the structure of an extended double. In this article, we prove that any singular superalgebra is algebraically generated and, therefore, has the structure of an extended double.

Zero product determined of amalgamated duplication of Banach algebras

In this paper, we study some sufficient and necessary conditions for the amalgamated duplication Banach algebra [Formula: see text] to be zero product determined. Precisely, we show that in the case where [Formula: see text] has a bounded approximate identity, [Formula: see text] is zero product determined if and only if [Formula: see text] is zero product determined and [Formula: see text] has the property [Formula: see text]. Moreover, we give a better characterization when [Formula: see text] is unital. As an application, we also construct some examples on semidirect product of Banach algebras and the [Formula: see text]–Lau product of Banach algebras. Finally, we raise some open problems related to the zero product determined of classical module extension Banach algebras.

Lie (Jordan) $ \sigma- $centralizer at the zero products on generalized matrix algebra

<p>Given a unital commutative ring $ \mathscr{R} $, $ (\mathscr{A}, \mathscr{B}) $ and $ (\mathscr{B}, \mathscr{A}) $ are bimodules of $ \mathscr{M} $ and $ \mathscr{N} $, respectively, where $ \mathscr{A}, \mathscr{B} $ are unitals $ \mathscr{R}- $algebras. The $ \mathscr{R}- $algebra $ \mathscr{G} = $ $ \mathscr{G}(\mathscr{A}, \mathscr{M}, \mathscr{N}, \mathscr{B}) $ is a generalized matrix algebra described by the Morita context $ (\mathscr{A}, \mathscr{B}, \mathscr{M}, \mathscr{N}, \zeta_{\mathscr{M}\mathscr{N}}, \chi_{\mathscr{N}\mathscr{M}}) $. The present study investigated the structure of Lie (Jordan) $ \sigma- $centralizers at the zero products on order two generalized matrix algebra and established that each Jordan $ \sigma- $centralizer at the zero products is a $ \sigma- $centralizer at the zero product on order two generalized matrix algebra. We also provided sufficient and necessary conditions under which a Lie $ \sigma- $centralizer at the zero product is proper on an order two generalized matrix algebra.</p>

Infrastructure, durability and sustainability in one concept

In this paper, the increase of the concrete structure durability is investigated through the implementation of restoration techniques aimed at achieving this goal through the use of specific advanced systems.Over time, concrete infrastructures are often subjected to the action of dynamic loads of variable amplitude that can establish different stress configurations. To this scope, a special fibre-reinforced cementitious mortar has been developed. This product has been subjected to small and large-scale dynamic bending tests and it has shown high fatigue properties.Concrete infrastructures can also be affected by different degradation phenomena that can occur depending on environmental exposure conditions. The most frequent phenomena certainly include carbonation and chloride attack. In this regard, this article shares Mapei’s experience with the use of elastic cementitious mortar, emphasising the high level of protection offered both in terms of protection against carbonation and against the ingress of chlorides.To this scope, numerous laboratory tests performed on these types of membranes are shared, as well as the tests performed on samples taken from existing structures, 18 years after application, for an in-depth evaluation of the durability increase over time.Finally, a small focus on a new range of Mapei products is carried out. The Mapei Zero product range has been the object of an important research and development work to reduce the carbon footprint of these materials underlining an increasing attention to environmental sustainability.

Exact Correlations in Topological Quantum Chains

Although free-fermion systems are considered exactly solvable, they generically do not admit closed expressions for nonlocal quantities such as topological string correlations or entanglement measures. We derive closed expressions for such quantities for a dense subclass of certain classes of topological fermionic wires (classes BDI and AIII). Our results also apply to spin chains called generalised cluster models. While there is a bijection between general models in these classes and Laurent polynomials, restricting to polynomials with degenerate zeros leads to a plethora of exact results: (1) we derive closed expressions for the string correlation functions - the order parameters for the topological phases in these classes; (2) we obtain an exact formula for the characteristic polynomial of the correlation matrix, giving insight into ground state entanglement; (3) the latter implies that the ground state can be described by a matrix product state (MPS) with a finite bond dimension in the thermodynamic limit - an independent and explicit construction for the BDI class is given in a concurrent work [Phys. Rev. Res. 3 (2021), 033265, 26 pages, arXiv:2105.12143]; (4) for BDI models with even integer topological invariant, all non-zero eigenvalues of the transfer matrix are identified as products of zeros and inverse zeros of the aforementioned polynomial. General models in these classes can be obtained by taking limits of the models we analyse, giving a further application of our results. To the best of our knowledge, these results constitute the first application of Day's formula and Gorodetsky's formula for Toeplitz determinants to many-body quantum physics.

A Class of Zero Product Determined Banach Algebras

A Class of Zero Product Determined Banach Algebras

Nonsurjective zero product preservers between matrix spaces over an arbitrary field

A map Φ between matrices is said to be zero product preserving if Φ ( A ) Φ ( B ) = 0 whenever AB = 0. In this paper, we give concrete descriptions of an additive/linear zero product preserver Φ : M n ( F ) → M r ( F ) between matrix algebras of different dimensions over an arbitrary field F , and n ≥ 2 . In particular, we show that if Φ is linear and preserves zero products then Φ ( A ) = S ( R 1 ⊗ A 0 0 Φ 0 ( A ) ) S − 1 , for some invertible matrices R 1 in M k ( F ) , S in M r ( F ) and a zero product preserving linear map Φ 0 : M n ( F ) → M r − nk ( F ) into nilpotent matrices. If Φ ( I n ) is invertible, then Φ 0 is vacuous. In general, the structure of Φ 0 could be quite arbitrary, especially when Φ 0 ( M n ( F ) ) has trivial multiplication, i.e. Φ 0 ( X ) Φ 0 ( Y ) = 0 for all X, Y in M n ( F ) . We show that if Φ 0 ( I n ) = 0 or r − nk ≤ n + 1 , then Φ 0 ( M n ( F ) ) indeed has trivial multiplication. More generally, we characterize subspaces V of square matrices satisfying XY = 0 for any X , Y ∈ V . Similar results for double zero product preserving maps are obtained.

Zero product determined n-th Schrödinger algebra

The n-th Schrödinger algebra schn:=sl2⋉hn is the semi-direct product of the Lie algebra sl2 with the n-th Heisenberg Lie algebra hn. Let K be an algebraically closed field of characteristic zero. A Lie algebra L is zero product determined over K, if for every K-linear space V and every bilinear map ϕ:L×L→V with the property that ϕ(x,y)=0 whenever [x,y]=0, then there exists a linear map f:[L,L]→V such that ϕ(x,y)=f([x,y]) for all x,y∈L. This article shows that the n-th Schrödinger algebra schn is zero product determined. Applying this result, product zero derivations and two-sided commutativity-preserving maps on schn are determined. Furthermore, quasi-derivations, linear anti-commuting maps, quasi-automorphisms and strong commutativity-preserving maps of schn are all obtained.

Earth, Water, Air, and Fire – Thinking about Farming and Farmscapes

Farming has changed the face of the earth in Africa as much as elsewhere. But histories of African farmscapes, shaped by millennia of agriculture, are obscured by narratives of pristine landscapes, whether of forests or savanna, and the role of farming in transforming African farmscapes is seldom taught in schools. We present examples of farming strategies and systems from western and southern Africa, which we hope are inspiring and maybe, at times, even surprising. Our exploration of the farmscapes, structured along the classical elements of Earth, Fire, Water, and Air, describes how plants and people deal with the influence these elements have on successful farming and how these influences show up in farmscapes. We hope these stories of flexibility, adaptation, and success and failure motivate teachers and students to think out of the box in grappling with the challenges our world is facing. These stories also provide opportunities for teaching about the United Nations Sustainable Development Goals (SDGs), particularly the goals of Zero Hunger (SDG 2), Responsible Consumption and Production (SDG 12), and Life on Land (SDG 15).

A GENDER PERSPECTIVE IN MITIGATING FALL ARMYWORM (Spodoptera frugiperda) TOWARDS ENVIRONMENTAL AND FOOD PRODUCTION RESILIENCE IN BOMET COUNTY, KENYA

The emergence and rapid spread of the fall armyworm (FAW) Spodoptera frugiperda in Africa having spread from its Native American since 2016 seriously threatens the food crop production of millions of smallholder farmers. In December 2016, the Kenyan government started experiencing the invasion of FAW threatening the food crop production in the country. Smallholder farmers have different household setups with gender differentials towards managements of any new invasive crop pests including FAW. From literature reviews, fall armyworm invasion can affect food production to zero production if not properly managed but there are gaps on effects of fall armyworm within different headed households by gender prompting the study on effects of fall armyworm invasion on food production between differentiated headed households in Bomet County, Kenya. Data was collected using multiple approaches including interviews on households and key informants, focus group discussions and observations. A household baseline survey and focus group discussions were done using a structured questionnaire and checklist where a total of 384 respondents were enumerated. The study result showed that the management of fall armyworm are gender specific with different gender roles and activities being used. Therefore, gender specific programs and different headed households should be approached differently during agricultural production using an effective network of extension and advisory which provides technical advice on management of new invasive pests towards food production and environmental resilience

A narrative action on the battle against hunger using mushroom, peanut, and soybean-based wastes.

Numerous generations have been affected by hunger, which still affects hundreds of millions of people worldwide. The hunger crisis is worsening although many efforts have been made to minimize it. Besides that, food waste is one of the critical problems faced by most countries worldwide. It has disrupted the food chain system due to inefficient waste management, while negatively impacting the environment. The majority of the waste is from the food production process, resulting in a net zero production for food manufacturers while also harnessing its potential. Most food production wastes are high in nutritional and functional values, yet most of them end up as low-cost animal feed and plant fertilizers. This review identified key emerging wastes from the production line of mushroom, peanut, and soybean (MPS). These wastes (MPS) provide a new source for food conversion due to their high nutritional content, which contributes to a circular economy in the post-pandemic era and ensures food security. In order to achieve carbon neutrality and effective waste management for the production of alternative foods, biotechnological processes such as digestive, fermentative, and enzymatic conversions are essential. The article provides a narrative action on the critical potential application and challenges of MPS as future foods in the battle against hunger.

On simple left-symmetric algebras

We prove that the multiplication algebra M(A) of any simple finite-dimensional left-symmetric nonassociative algebra A over a field of characteristic zero coincides with the right multiplication algebra R(A). In particular, A does not contain any proper right ideal. These results immediately give a description of simple finite-dimensional Novikov algebras over an algebraically closed field of characteristic zero [29].The structure of finite-dimensional simple left-symmetric nonassociative algebras from a very narrow class A of algebras with the identities [[x,y],[z,t]]=[x,y]([z,t]u)=0 is studied in detail. We prove that every such algebra A admits a Z2-grading A=A0⊕A1 with an associative and commutative A0. Simple algebras are described in the following cases: (1) A is four dimensional over an algebraically closed field of characteristic not 2, (2) A0 is an algebra with the zero product, and (3) A0 is simple; in the last two cases, the description is given in terms of root systems. A necessary and sufficient condition for A to be complete is given.

Exploring Sustainability Implications of Transitions to Agroecology: a Transdisciplinary Perspective

SummarySuccessful transitions to agroecology require shared understanding of the sustainability implications of transitions for food systems. To gain such understanding, a transdisciplinary approach is increasingly called for by funders, end users of research and scientists. Transdisciplinary processes were used in the UNISECO project to develop strategic pathways that enable transitions to agroecology in case studies across Europe. These strategic pathways were combined with scenarios of EU food systems in 2050, in which combinations of agroecological farming and food consumption practices were assessed. These were then reviewed considering selected UN Sustainable Development Goals (SDGs) as a reference for discussing the sustainability implications of transitions to agroecology. Sustainability implications were identified for several SDGs including Zero Hunger (SDG 2), Quality Education (SDG 4), Responsible Consumption and Production (SDG 12), Climate Action (SDG 13) and Life on Land (SDG 15). Key factors contributing to the sustainability of transitions to agroecology are: i) mature social capital and improved farmer knowledge of the benefits of agroecological practices; ii) strengthened collaborative actions and collective institutions to increase negotiating power within the value‐chain; and, iii) changes in consumer behaviour and diets. These factors highlight the need for a food system perspective in transitions to agroecology and supporting policies. This in turn highlights the meaningful role of transdisciplinary research in strengthening the sustainability of European food systems.

Industry 5.0 and the Circular Economy: Utilizing LCA with Intelligent Products

While the move towards Industry 4.0 has motivated a re-evaluation of how a manufacturing organization should operate in light of the availability of a new generation of digital production equipment, the new emphasis is on human worker inclusion to provide decision making activities or physical actions (at decision nodes) within an otherwise automated process flow; termed by some authors as Industry 5.0 and seen as related to the earlier Japanese Society 5.0 concept (seeking to address wider social and environmental problems with the latest developments in digital system, artificial Intelligence and automation solutions). As motivated by the EU the Industry 5.0 paradigm can be seen as a movement to address infrastructural resilience, employee and environmental concerns in industrial settings. This is coupled with a greater awareness of environmental issues, especially those related to Carbon output at production and throughout manufactured products lifecycle. This paper proposes the concept of dynamic Life Cycle Assessment (LCA), enabled by the functionality possible with intelligent products. A particular focus of this paper is that of human in the loop assisted decision making for end-of-life disassembly of products and the role intelligent products can perform in achieving sustainable reuse of components and materials. It is concluded by this research that intelligent products must provide auditable data to support the achievement of net zero carbon and circular economy goals. The role of the human in moving towards net zero production, through the increased understanding and arbitration powers over information and decisions, is paramount; this opportunity is further enabled through the use of intelligent products.

Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

Two-sided zero product properties on symmetric algebras

We characterize bilinear functionals ϕ on a symmetric algebra A satisfying the two-sided zero product property (the 2-zpp, i.e., ϕ(x,y)=0 whenever xy=yx=0). If A is also a zero product determined algebra and if every derivation of the algebra A is inner, then A is a 2-zpd algebra (i.e., every bilinear functional on A satisfying the 2-zpp is of the form (x,y)↦τ1(xy)+τ2(yx) for x,y∈A, where τ1,τ2 are linear functionals on A). Conversely, if A is a finite-dimensional 2-zpd algebra, then the derivations of A are characterized, that is, given any derivation d of the algebra A, there exists a∈A such that, for all x∈A, d(x)−[a,x] lies in the Jacobson radical of A. Finally, we determine all bilinear functionals satisfying the 2-zpp on a specific zpd symmetric algebra and hence decide whether such an algebra is 2-zpd.

Fixed product preserving mappings on Banach algebras

In this paper, we describe linear maps between complex Banach algebras that preserve products equal to fixed elements. This generalizes some important special cases where the fixed elements are the zero or identity element. First we show that if such map preserves products equal to a finite-rank operator, then it must also preserve the zero product. In several instances, this is enough to show that a product preserving map must be a scalar multiple of an algebra homomorphism. Second, we explore a more general problem concerning the existence of product preserving maps and the relationship between the fixed elements. Lastly, motivated by Kaplansky's problem on invertibility preservers, we show that maps preserving products equal to fixed invertible elements are either homomorphisms or antihomomorphisms multiplied on the left by a fixed element.