Proof. First note that the map φ is uniquely determined by its components φ11, φ12, φ21, φ22. Indeed, by the universal property of the coproduct M1 ⊕ M2 we see that φ is uniquely determined by the maps φ∗1 := φ◦ι1 and φ∗2 := φ◦ι2. Then from the universal property of the product N1⊕N2 we see that the map φ∗1 is uniquely determined by the maps φ11 = π1 ◦φ∗1 and φ21 = π2 ◦ φ∗1. Similarly, φ∗2 is u...

for −∞ < z < ∞. The properties of this distribution and its generalizations have been studied by several authors. Of particular eminence are the numerous papers on this topic by Professor N. Balakrishnan and his colleagues; see, for example, Balakrishnan [1, 2, 3], Balakrishnan and Aggarwala [4], Balakrishnan et al. [5, 7, 12], Balakrishnan and Chan [6], Balakrishnan and Joshi [8], Balakrishnan...

We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M , generalizing a result of Dolich on o-minimal theories in [4].

In ring theory, the notion of annihilator is an important tool for studying the structures. Many characterizations and structure theorems can be derived by using this notion. On the other hand, certain classes of rings (e.g., Baer rings and Rickart rings) are defined by considering annihilators ideals. In the present work, we introduce a class of rings which is close to the class of Rickart rin...

While environmental pollution is becoming more and more serious, many countries are adopting policies to control pollution. At the same time, the environmental regulation will inevitably affect economic and social development, especially employment growth. The environmental regulation will not only affect the scale of employment directly, but it will also have indirect effects by stimulating up...

هدف: این پژوهش با هدف ارائه مدل چالش‌های پرورش کودکان کم‌شنوای پیش‌دبستانی از دیدگاه مادران و متخصصان بر اساس نظریه داده‌بنیاد انجام ‌شده است. روش: نمونه 15 مادر کودک کم‌شنوا 4 تا 6 ساله انجمن والدین شهر تهران 5 متخصص حوزه ناشنوا بودند که در سال 1400 استفاده روش نمونه‌گیری هدفمند انتخاب شدند. چالش ­های طریق مصاحبه نیمه ساختاریافته عمیق رسیدن به اشباع نظری جمع‌آوری کدگذاری (کدگذاری باز، محوری ان...

Background in music performance research For the past few decades there has been considerable scientific interest in expression in music performance (Gabrielsson, 2003). A particularly relevant aspect of music performance is expressive timing, that is, the fluctuations of tempo during a performance. Accordingly, expressive timing has been one of the major topics in music performance research. A...