Some sum–product type estimates for two-variables over prime fields

AbstractLet {\mathcal{R}} be a finite valuation ring of order {q^{r}}. In this paper, we prove that for any quadratic polynomial {f(x,y,z)\in\mathcal{R}[x,y,z]} that is of the form {axy+R(x)+S(y)+T(z)} for some one-variable polynomials {R,S,T}, we have|f(A,B,C)|\gg\min\biggl{\{}q^{r},\frac{|A||B||C|}{q^{2r-1}}\bigg{\}}for any {A,B,C\subset\mathcal{R}}. We also study the sum-product type problems over finite valuation ring {\mathcal{R}}. More precisely, we show that for any {A\subset\mathcal{R}} with {|A|\gg q^{r-\frac{1}{3}}} then {\max\{|AA|,|A^{d}+A^{d}|\}}, {\max\{|A+A|,|A^{2}+A^{2}|\}}, {\max\{|A-A|,|AA+AA|\}\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}}, and {|f(A)+A|\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}} for any one variable quadratic polynomial f.

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Donation or Discount: Effect of Promotion Mode on Green Consumption Behavior

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph18041912 ◽

2021 ◽

Vol 18 (4) ◽

pp. 1912

Author(s):

Jun Zou ◽

Yifan Tang ◽

Ping Qing ◽

Han Li ◽

Amar Razzaq

Keyword(s):

Purchase Intention ◽

Environmental Issues ◽

Environmental Problems ◽

Product Type ◽

Mediation Effect ◽

Green Consumption ◽

Consumption Behavior ◽

Conceptual Fluency ◽

Global Concern ◽

Practical Implications

Environmental issues are still challenging and of global concern. To improve the environmental consumption behavior of consumers, this study investigates whether the match between the promotion mode and product type can improve the conceptual fluency of consumers, so as to increase their purchase intention for green products. The results of three experiments reveal that the interaction between promotion mode and product type has a certain impact on the conceptual fluency of consumers, which can, in turn, promote their purchase intention. This research theoretically contributes to the research on green consumption by introducing promotion mode and revealing the mediation effect of conceptual fluency, it also provides some practical implications for alleviating environmental problems.

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Designing and Distinguishing Meaningful Artisan Food Experiences

Sustainability ◽

10.3390/su13158569 ◽

2021 ◽

Vol 13 (15) ◽

pp. 8569

Author(s):

Erin Percival Carter ◽

Stephanie Welcomer

Keyword(s):

Product Information ◽

Food Products ◽

Well Being ◽

Product Type ◽

Target Market ◽

High Involvement ◽

Consumer Expectations ◽

Typical Food ◽

The Relationship ◽

Additional Product

We examine consumer expectations about how specialty versus conventional food products affect well-being and how small, artisan producers can use that information to design better customer experiences. Drawing on recent work examining the costs and benefits of pleasure- and meaning-based consumption, we investigate whether consumer expectations that specialty products are more meaningful lead to increased desire for additional product information. We selectively sampled from the target market of interest: high-involvement consumers who regularly consume a food (cheese) in both more typical and specialty forms. The authors manipulate product type (typical versus special) within participant and measure differences in expected pleasure and meaning as well as a variety of behaviors related to and preference for additional product information. We find that these high-involvement consumers expect special food products to provide both more meaningful (hypothesized) and more pleasurable consumption experiences (not hypothesized) than typical food products. Consistent with our theory, consumer use of, search for, and preference for additional product information was greater for special products. A causal mediation analysis revealed that expectations of meaning mediate the relationship between product type and utility of product information, an effect which persists controlling for the unexpected difference in expected pleasure.

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