Complementation and decompositions in some weakly Lindelöf Banach spaces

AbstractLet Γ denote an uncountable set. We consider the questions if a Banach space X of the form C(K) of a given class (1) has a complemented copy of c0(Γ) or (2) for every c0(Γ)⊆X has a complemented c0(E) for an uncountable E⊆Γ or (3) has a decomposition X=A⊕B where both A and B are nonseparable. The results concern a superclass of the class of nonmetrizable Eberlein compacts, namely Ks such that C(K) is Lindelöf in the weak topology and we restrict our attention to Ks scattered of countable height. We show that the answers to all these questions for these C(K)s depend on additional combinatorial axioms which are independent of ZFC±CH. If we assume the P-ideal dichotomy, for every c0(Γ)⊆C(K) there is a complemented c0(E) for an uncountable E⊆Γ, which yields the positive answer to the remaining questions. If we assume ♣, then we construct a nonseparable weakly Lindelöf C(K) for K of height ω+1 where every operator is of the form cI+S for c∈R and S with separable range and conclude from this that there are no decompositions as above which yields the negative answer to all the above questions. Since, in the case of a scattered compact K, the weak topology on C(K) and the pointwise convergence topology coincide on bounded sets, and so the Lindelöf properties of these two topologies are equivalent, many results concern also the space Cp(K)

Russo-Ukrainian War Effects on Brown-Forman Finland Supply Chain Operations

We live in a very concerning time since now there has been going on war for more than year and-a half between Russia and Ukraine, which has affected millions of people’s lives. Russo Ukrainian war has negatively also affected lots of businesses. Author decided to investigate further on how Russo-Ukrainian war has affected the supply chains and its operations of Brown Forman Finland (BFF). This research analysed the current supply chain operational performance and the effects of Russo-Ukrainian war on the supply chain operations of Finlandia Vodka at Brown-Forman Finland. The aim was to analyse the effects of Russo-Ukrainian war on BFF’s supply chain operations and how can BFF prepare for future crises. By doing so, the company can see the effects of war on its supply chain operations, improve the supply chain operations and be prepared for any future crises by creating good contingency plan and crisis strategy. The author chose to focus the research on the interpretation of numerical data and on the overall structure of the supply chain processes. The primary data was collected while working as a Logistics Specialist at the company. There were also several meetings with the company’s Managing Director, Sami Pulkkinen. The secondary data used for analyses was comprised of the company’s own data, which was related to the company’s supply chain operation’s performance results. The findings revealed that the Russo-Ukrainian war had negative impact on Brown-Forman Finland’s supply chain operations. Many important supply chain performance metrics and supply chain operations were affected negatively by the Russo-Ukrainian war. The research also revealed that Brown-Forman Finland’s supply chain operations, emergency strategy and contingency plan needs to be improved to stay prepared for any future crises

Traktorid T-40 ja T-40A

Traktoriehitus Nõukogude Liidus on viimastel aastatel tunduvalt edasi arenenud. Traktorite konstruktsiooni täiustamisel peetakse silmas töökindluse suurendamist, mugavamat juhtimist, paremaid ekspluatatsiooniomadusi jne. Mitmeid sõlmi ja agregaate on viimastel aastatel täiendatud ja parandatud ka traktoritel T-40 ja T-40A ning see töö jätkub pidevalt. Arvestades ülalnimetatud asjaolusid on käesolevat raamatut originaaliga võrreldes mitmetes osades muudetud ja täiendatud, kusjuures algallikatena on kasutatud Lipetski Traktoritehases toodetavate traktorite kohta väljaantud ekspluatatsioonijuhendeid. Raamatust on välja jäetud peatükk, milles kirjeldatakse traktorite T-40 ja T-40A kasutamist ja agregateerimist üksikutel põllumajanduslikel töödel, sest mitmed selles kirjeldatud masinad on vananenud konstruktsiooniga ja väljatöötuse ökonoomilise arvestuse aluseks on tingkünnihektar, mis praegu enam ei kehti. Raamatule on lisatud traktorite T-40 ja T-40A uute modifikatsioonide lühike kirjeldus, milles on toodud nende ehituse ja hooldamise mõningad iseärasused. Toimetaj