Sentence examples for and cannot be attained from inspiring English sources

The original Carlson inequality [5] is as follows: ∑ k = 1 ∞ a k 2 ≤ π ∑ k = 1 ∞ a k 2 1 / 2 ∑ k = 1 ∞ k 2 a k 2 1 / 2, (6.1 where the constant π is sharp and cannot be attained at a non identically zero sequence { a k } k = 1 ∞.

They come with the confusing baggage of mixed feelings and paradoxical emotions, and recovery cannot be attained without correct therapeutic intervention and time.

Who joins the union is Europe's affair, he said, adding: "But many people will agree with me when I say that prosperity, stability, security and integration cannot be attained at the expense of the others.

As a result of this dependence, steady state polynya edge solutions exist that support seemingly unrealistic corners and that cannot be attained by evolving the polynya equations from an initial state in which the polynya is closed.

Conditions (i) and (ii) cannot be attained simultaneously if (Dle1).

However, as biliary and pancreatic sphincterotomy and stent placement cannot be attained during EUS, those who require these therapeutic interventions must also undergo an ERCP.

The analysis and rearrangement of facts which is indispensable to the growth of knowledge and power of explanation and right classification cannot be attained purely mentally — just inside the head.

IV injections should only be used in an emergency like in the advanced stages of milk fever, grass tetany, or if a calf is in need of fluids and electrolytes which cannot be attained as quickly from oral administration.

The cocrystallization of P LLA-co-L-2HB) coP LLA-co-L-2HBP LLA-co-L-2HBide the versatile biodegradable materials having a wide variety of degradation rates and behavior by altering the monomer unit contents and also by crystallinity and crystalline size which cannot be attained by non-crystallizable biodegradable coP LLA-co-L-2HBill thereby widen the applicopolymers LLA-based polymers.

Indeed, the Millennium Development Goals to improve maternal health, reduce child mortality, promote gender equality and empower women and eradicate extreme poverty cannot be attained without a specific focus on women's mental health [ 47].

Petitioners urge that sections 4(a) and 5 'merely implement the system of controls'; that the policy of the act as declared in section 1(c), 15 U.S.C.A. § 79a(c), is to compel 'the simplification and the elimination of holding company systems'; and that the objective cannot be attained by informatory processes but only by such regulation or control as will 'eliminate' the evils.